Twistorial superparticle with tensorial central charges
A twistorial formulation of the N=1 D=4 superparticle with tensorial central charges describing massive and massless cases in uniform manner is given. The twistors resolve energy-momentum vector whereas the tensorial central charges are written in term of spinor Lorentz harmonics. The model makes po...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2001 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2001
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/79424 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Twistorial superparticle with tensorial central charges / S.A. Fedoruk, V.G. Zima // Вопросы атомной науки и техники. — 2001. — № 6. — С. 60-64. — Бібліогр.: 14 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860204238062223360 |
|---|---|
| author | Fedoruk, S.A. Zima, V.G. |
| author_facet | Fedoruk, S.A. Zima, V.G. |
| citation_txt | Twistorial superparticle with tensorial central charges / S.A. Fedoruk, V.G. Zima // Вопросы атомной науки и техники. — 2001. — № 6. — С. 60-64. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | A twistorial formulation of the N=1 D=4 superparticle with tensorial central charges describing massive and massless cases in uniform manner is given. The twistors resolve energy-momentum vector whereas the tensorial central charges are written in term of spinor Lorentz harmonics. The model makes possible to describe states preserving all allowed fractions of target-space supersymmetry. The full analysis of the number of conserved supersymmetries in models with N=1 D=4 superalgebra with tensorial central charges has been carried out.
|
| first_indexed | 2025-12-07T18:11:39Z |
| format | Article |
| fulltext |
TWISTORIAL SUPERPARTICLE
WITH TENSORIAL CENTRAL CHARGES
S.A. Fedoruk1, V.G. Zima2
1Ukrainian Engineering Pedagogical Academy, Kharkov, Ukraine
e-mail: fed@postmaster.co.uk
2Kharkov National University, Kharkov, Ukraine
e-mail: zima@postmaster.co.uk
A twistorial formulation of the N=1 D=4 superparticle with tensorial central charges describing massive and
massless cases in uniform manner is given. The twistors resolve energy-momentum vector whereas the tensorial
central charges are written in term of spinor Lorentz harmonics. The model makes possible to describe states
preserving all allowed fractions of target-space supersymmetry. The full analysis of the number of conserved
supersymmetries in models with N=1 D=4 superalgebra with tensorial central charges has been carried out.
PACS: 11.15.-q, 11.17.+y, 02.40.+m, 11.30.Pb
1. INTRODUCTION
Some interesting supersymmetric theories admit as
scalar central charges, which are presented in the
conventional Poincare supersymmetry, as well as the
nonscallar ones [1]. In the supersymmetry algebra
tensorial central charges are usually associated with
topological contributions of extended objects. It is
attractive to consider the pure superparticle models
having symmetry of this kind. Such a model was firstly
obtained in massless case with two or three local κ -
symmetries [2]. We have constructed the model of
massive non-extended superparticle with central
charges [3] having single κ -symmetry, which is
equivalent to conventional spinning (spin 1/2) particle.
In a certain sense the commuting spinor variables of the
model play the role of index spinor variables [4], [5].
Analogous model of massive superparticle has been
formulated in [6,7] without Lorentz invariance. In fact
the model [6,7] is obtained in particular case of
model [3] with constant index spinor fixed in non-
Lorentz invariant way.
In recent work [8] we proposed twistorial
formulation of superparticle with tensorial central
charges in which massive and massless cases are
described uniformly. The model uses both central
charge coordinates and auxiliary bosonic spinor
variables simultaneously. In term of the last variables
the energy-momentum vector and the tensorial central
charges are resolved. In the massive case of the
proposed model we have twistorial formulation of
massive superparticle with tensorial central charges
preserving 1/4 or 1/2 of target-space supersymmetries.
For zero mass this model turns into twistorial
formulation of the massless superparticle with tensorial
central charges [2] in which one or two of target-space
supersymmetries are broken. But the case of massless
superparticle with only one κ -symmetry is impossible
in this formulation.
Our purpose here will be to give twistorial
formulation of N=1 D=4 superparticle with tensorial
central charges which is able to describe massive and
massless cases in a uniform manner with all allowed
possibilities of the target-space supersymmetry
violation. In addition to twistors we use pair of
harmonic spinors by means of which the tensorial
central charges are resolved in Lorentz-covariant way.
But in some cases the choice of corresponding gauges
makes possible to remain only with one type of spinors,
for example, with twistors.
We will in section 2 investigate the D=4 N=1
superalgebra with tensorial central charges with respect
to all allowed parts of unbroken target-space
supersymmetry depending on the value of the
momentum square (particle mass). Section 3 presents
the twistor formulation of D=4 N=1 superparticle with
tensorial central charges. Excepting twistor spinors we
use Lorentz harmonics also. Section 4 describes
possible sets of tensor central charges coefficients in
particle action and corresponding interconnection of
harmonic and twistor spinors. Section 5 contains some
comments.
2. SUPERALGEBRA WITH TENSORIAL
CENTRAL CHARGES
Generalized central extension of nonextended 4-
dimensional supersymmetry algebra with Majorana
supercharges Q can be written in the form
Ζ= 2},{ QQ .
Here Ζ=Ζ T is the matrix of central charges with a
total of ten real entries. We have tensorial central
charges as coefficients in decomposition of this matrix
µ ν
µ ν
µ
µ γγ ZiPC )(
2
)( +=Ζ
on the basis defined by products of γ -matrices. The
vector µP is (in general) a sum of the energy-
momentum vector and a vectorial ‘string charge’.
Namely this vector plays the role of particle energy-
60 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2001, № 6, p. 60-64
momentum in considering theory. In follows we
suppose what the vector µP satisfies spectral property,
i.e. it is positive time-like or light-like four-vector;
22 mP −= , where m is mass. Six real charges
ν µµ ν ZZ −= are related to the symmetric complex Weyl
spin-tensor β αα β ZZ = in standard way. The spin-
tensors α βZ and )( α ββα ZZ = represent the self-dual
and anti-self-dual parts of the central charge matrix.
The l.h.s. of the equation for eigenvalues of the
matrix Ζ ,
0)det()( =−Ζ≡Π λλ ,
can be written as a polynomial [1] in λ ,
k
kk λλ Π∑=Π =
4
0)( ,
with
cbPaP 48])[( 0
22
00 −+−=Π ,
baPP 8])[(4 2
001 +−=Π ,
])(3[2 2
02 aP −=Π ,
03 4P=Π ,
14 =Π .
Here
222 PHEa
++= ,
)( HEPb
×= ,
222 |||||| HEHPEPc
×+×+×=
and
,0i
i ZE = jk
ijki ZH ε
2
1=
are electric and magnetic vectors of tensorial central
charges.
For the case of massive particle, in the rest frame
where 0=P
and mP =0 , we can choose the first axis
along the vector E
if it is nonzero. The second axis is
embedded in a half-plane defined by the vector H
with
respect to E
. In the massless case if 0≠HE
one can
take HE
|| without loss of generality. If 0=HE
one
can choose 0=H
for 022 >− HE
and 0=E
for
022 <− HE
.
The massive superparticle with unique preserved
SUSY ( 00 =Π , 01 ≠Π ) is obtained only if
0||4)( 22222 ≠×=−− HEHEm
.
Up to rotations the variety of such configurations is
characterised by positive modulus of non-collinear
vectors E
and H
and the angle ϑ between them. At
the boundary of this region of parameters when
0222 ≠+= HEm
with collinear E
and H
we have
two preserved SUSYs ( 010 =Π=Π , 02 ≠Π ).
Conditions for preserving more than two SUSYs (
0210 =Π=Π=Π ) in massive case are contradictory.
In massless case there are two types of
configurations preserving unique SUSY. One of them
takes place for the collinear E
and H
with non-
collinear to them P
if 0sin4 2222 ≠=+ ϕPHE
where ϕ is the angle between P
and E
. Another one
consists in mutual orthogonality of three vectors E
, H
and P
forming right triple, 0>HEP
, and equality of
two modulus, 0|||| PHE ≠=
. At the boundary of the
first of these regions we have the odd sector of
conventional massless superparticle without central
charges ( 0== HE
) preserving two SUSYs. We have
two preserved SUSYs also if three mutually orthogonal
vectors E
, H
and P
form left triple 0<HEP
and
two of them have equal lengths
0|||| PHE ≠=
.
At the boundary of this region if mutually orthogonal
vectors form left triple and all of them have equal
modulus
0|||| PHE ==
,
then three SUSYs are preserved. All the SUSYs cannot
be preserved because of 04 03 ≠=Π P .
In the table all possible preservations of fractions of
target-space supersymmetry for massless ( 0=m ) and
massive ( 0≠m ) D=4 N=1 superparticle with tensorial
central charges are given. Except the case of massless
superparticle with ¼ unbroken SUSY, in Table 1 it is
mention the full set of necessary conditions. For
massless superparticle ( 0=m ) with ¼ unbroken SUSY
these conditions are complicated. We give required
conditions at orthogonal vectors E
, H
to P
,
0== HPEP
.
Here 1+=ε at 0>HEP
or 1−=ε at 0<HEP
.
In the following we present the twistorial
formulation of the superparticle with tensorial central
charges in which all allowed cases of supersymmetry
violation can be realized both for massive superparticle
and massless one.
The conditions on ‘electric’ and ‘magnetic’ vectors
of tensorial central charges and energy-momentum
vector for states of N=1 D=4 massless ( 0=m ) and
massive ( 0≠m ) superparticles preserving fractions ¼,
½ and ¾ of target-space supersymmetry
¼ ½ ¾
m
=0
0=× HE
,
2
0
22 4PHE =+
)0( == HPEP
0=HE
, 022 =− HE
,
0== HPEP
,
0=HE
,
02|||| PHE ±=−
ε
)0( == HPEP
2
0
22
2
PHE ≠+
2
0
22
2
PHE =+
61
m
≠0 =−+ 2222 )( mHE
0||4 2 ≠×= HE
0=× HE
,
222 mHE =+
no
3. LAGRANGIAN OF TWISTORIAL
SUPERPARTICLE WITH TENSORIAL
CENTRAL CHARGES
A trajectory of superparticle is parameterized by the
usual superspace coordinates µx , αθ , αθ and
tensorial central charge coordinates β αα β yy = ,
)( α ββα yy = . For description of superparticle energy-
momentum we use the pair of bosonic spinors
(bitwistor) avα , )( a
a vv αα = , 2,1=a . The tensor
central charges are written in terms of even spinor
variables auα , )( a
a uu αα = , 2,1=a . We use D=4
Weyl spinor and σ -matrices conventions of [9] where
the metric tensor µ νη has mostly plus and
γ
α
γβνµ
βα δσσ −=
)( ~ . The indices a , b , c , … which are
carried by the spinors avα , avα as well as auα , auα , are
raised and lowered as )2(SU ones.
For description of the superparticle, both massless
and massive, with tensorial central charges we take the
action LdS τ∫= with Lagrangian [8] in twistor-like
form
.uuuuvvvv hhhh
ZZPL
λλλλ
βα
τβα
α β
τα β
µ
τµ
−−−−
−Π+Π+Π=
(1)
Here the one-forms
θθ σθθ στ µµµµ
τ
µ diiddxd +−=Π≡Π ,
)( βαα βα β
τ
α β θθτ didyd +=Π≡Π ,
)( βαβαβα
τ
βα θθτ diydd +=Π≡Π
are invariant under global supersymmetry
transformations
αα εδ θ = , αα εθδ = ,
θδ θ σθδθ σδ µµµ iix −= ,
)( βαα β δ θθδ iy = , )( βαβα θδθδ iy =
acting in the extended superspace parameterised by the
usual superspace coordinates µx , αθ , αθ and by the
tensorial central charge coordinates α βy , βα y .
In the action the quantities µP , β αα β ZZ = ,
)( α ββα ZZ = which play the role of the momenta for
µx , α βy , βα y are taken in the form
a
avvPP αα
µ
βαµβα σ == , (2)
ab
ba CuuZ βαα β = , ab
ba CuuZ βαβα = (3)
where abC , )( ab
ab CC = are symmetric constants. Thus
they are resolved in terms of bosonic Weyl spinors avα ,
avα and auα , auα .
The last terms in Lagrangian (1) are the sum of the
kinematic constraints for the even spinors
02 ≈−≡ mvvh a
a
v α
α , 02 ≈−≡ mvvh a
av
α
α
(4)
02 ≈−≡ a
a
u uuh α
α , 02 ≈−≡ a
au uuh α
α
(5)
with Lagrange multipliers.
Due to the constraints (4) which are equivalent to
a
bb
a mvv δα
α = , b
a
b
a mvv δα
α =
we have mv a =)det( α and
22 mPPP −=≡ µ
µ .
Thus the constant || m plays the role of the mass.
In both cases, massless and massive, we have
twistorial resolution [10] of energy-momentum vector in
term of bosonic spinors.
In the massless case ( 0=m ) the spinors 1
αv and
2
αv are proportional to each other 21
αα vv ∝ as the
consequence of the constraint (4) 021 =α
α vv .
The constraints (5) are equivalent to
a
bb
auu δα
α = , b
a
b
auu δα
α =
and they give 1)det( =auα . Thus the spinors auα , auα
play the role of harmonic variables [11-13]
parametrizing an appropriate homogeneous subspace of
the Lorentz group.
In addition to kinematical constraints (4), (5) the
bosonic spinor variables of the model are satisfied to
constraints on spinor momenta ,0≈vp 0≈up and c.c.
A part of these constraints conjugate to constraints (2-5)
and are second class constraints. The rest of the
constraints on spinor momenta, which conserve the
constraints (2), (3), are first class constraints and
correspond to stability subgroup of Lorentz group acting
on indices a , b ,… The choices of gauge allow to
connect harmonic spinors and twistor ones for certain
cases of the central charges and particle mass.
4. SUPERPARTICLE STATES PRESERVING
ARBITRARY FRACTIONS OF TARGET-
SPACE SUPERSYMMETRY
The expressions (3) of central charges containing
three complex (six real) constants are collected in abC ,
abC . The symmetric matrices are expanded in
symmetric Pauli matrices
c
aiacabi )()( σεσ = , b
ci
acab
i )()( σεσ = ,
where b
ai )(σ , 3,2,1=i are usual Pauli matrices. Thus
abiiab CC )(σ= , ab
ii
ab CC )(σ−=
where )( ii CC = . We obtain directly
62
c
a
c
aii
bc
ab HEiHECCCC δδ )2( 22
+−=−= ,
)(22 22 HECCCC ii
ab
ab
+== ,
where real 3-vectors E
and H
are defined by the
equality
)( HiEiC
+= .
The vectors E
and H
are ‘electric’ and ‘magnetic’
vectors of tensorial central charges, which was used in
Section 2. But now they are determined with respect to
the basis of Lorentz harmonics auα , auα . In this basis
the components of energy-momentum are
a
aPP
2
1)0( = , a
bi
b
a
i PP )(
2
1)( σ=
where matrices b
aP and βα P are connected by the
Lorentz transformation generated by harmonic matrix
auα , i.e.
b
ab
a PuuP βαβα = .
Thus the condition
a
ab
ab
a vvPuu βαβα = (6)
connects bitwistor representation of the energy-
momentum and its representation in harmonic basis.
For given energy-momentum vector P the
fraction of preserving supersymmetry is determined by
the choice of ‘electric’ E
and ‘magnetic’ H
vectors.
Since central charges are written in terms of harmonics,
any choice of E
and H
does not lead to violation of
Lorentz invariance. In the following it is convenient to
make the analysis in the standard momentum frame.
Massive ( 0≠m ) case
In the frame of standard momentum mP =)0( ,
0)( =iP the expression (6) gives
a
a
a
a vvuum βαβα = .
Hence the harmonic spinors auα and twistor ones avα
are identical up to unitary transformations acting on
index a . Without loss of generality we can take
aa vum αα =2/1 .
This identification can be obtained by gauge fixing of
the harmonic degrees of freedom, which are pure gauge
ones in the initial action (1). As result, we derive the
model of superparticle with only twistor spinors (or only
with Lorentz harmonics). Such model was considered in
[8] and gives all possible cases of target-space
supersymmetry preserving for massive superparticle.
The case with ½ unbroken SUSY is reached if
central charge coefficients satisfy the conditions
22mCC ab
ab = , 44mCCCC cd
cd
ab
ab = (7)
which are equivalent to
222 mHE =+
, 0=× HE
.
As it been obtained in [8], the conditions (7) give the
unitary condition on the coefficient matrix of central
charges
c
a
bc
ab mCC δ2= .
Without loss of generality we can take diagonal matrix
abC with m multiplied on phase multipliers on
diagonal of them. This corresponds to vectors E
and
H
which both set in plane XY .
The case with ¼ unbroken SUSY is obtained for
0≠× HE
when
||2|| 222 HEmHE
×=−+
is satisfied. Here only one from two elements of
diagonal matrix abC has the modulus equal to m .
Massless ( 0=m ) case
In the standard energy-momentum frame for
massless particle
),0,0,( )0()0( PPP =µ
and
b
a
b
a PP )(2 )0(
+= σ
where 2/)1( 32 σσ +=+ . The twistor spinors, which
are proportional each other in massless case can be
taken equal
21
ααα vvv =≡ .
Then the expression (6) give
βαβα vvuuP 22 1
1)0( = .
Therefore one harmonic spinor 1
αu is expressed in form
twistor one αv up to phase transformation. Thus we can
remain with twistor spinor αv and one harmonic spinor
2
αu . The second harmonic spinor is obtained directly
from twistor one (for example, αα vPu 2/1)0(1 )( −= ) if it
is necessary.
In terms of vectors E
and H
the matrix abC has
the following expression
−−−−+−
+−+−−
=
)(
)(
122133
331221
EHiEHiEH
iEHEHiEH
Cab .
In case of ½ and ¾ unbroken SUSY vectors E
and
H
are orthogonal to each other and to vector P
(see
Table 1) which along third axis. Therefore
033 == HE and matrix abC is diagonal. In these cases
(½ and ¾ unbroken SUSY) vectors E
and H
have
equal lengths VHE ≡= ||||
and the nonzero elements
of the matrix abC are φiVeC −= 211 in case 0>HEP
or
φiVeC 222 −= in case 0<HEP
where φ is angle
between first axis and vector H
. In case of ½ unbroken
SUSY it is just )0(PV ≠ whereas in case of ¾ unbroken
SUSY it is fulfilled )0(PV = . The case with 0>HEP
63
and nonzero only 011 ≠C correspond to twistor model
of the superparticle with tensorial central charges
considered in [2].
For massless particle the states which preserving ¼
SUSY are realised at |||| HE
≠ when 0=HE
. At
these conditions the matrix abC has two nonzero
diagonal elements. Namely
φieHEC −+= |)||(|11
, φieHEC |)||(|22
−=
in case 0>HEP
or
φieHEC −−−= |)||(|11
, φieHEC |)||(|22
+−=
in case 0<HEP
. Thus the case with only one κ -
symmetry is realised for massless superparticle if two
spinors are presented in model. The using of one twistor
spinor as in [2] is insufficient for realization of ¼
unbroken SUSY. The more strong violation of target-
space supersymmetry requires using more numbers of
the spinors represented central charges of
supersymmetry algebra [14].
5. CONCLUSION
In present paper we construct the model of N=1 D=4
superparticle with tensorial central charges. By
corresponding choice of tensorial central charges we
obtain all possibilities of violated target-space
supersymmetry. It should be noted that these choices are
fulfilled in Lorentz-covariant way due to using Lorentz
harmonics in model.
The twistor formulation of the massive superparticle
is required to use of pair of twistors. For massless
superparticle the cases with ¾ and ½ unbroken SUSY
are realized by using only one twistor spinor, the
energy-momentum and the tensorial central charges are
resolved in form of which. But for realization of only ¼
unbroken SUSY it is necessary to use two spinors in
model, one from which is twistor whereas second used
spinor can be harmonic one.
This work was supported in part by INTAS Grant
INTAS-2000-254 and by the Ukrainian National Found
of Fundamental Researches under the Project
№ 02.07/383. We would like to thank I.A. Bandos,
A. Frydryszak, E.A. Ivanov, S.O. Krivonos,
J. Lukierski, A.J. Nurmagambetov and D.P. Sorokin for
interest to the work and for many useful discussions.
REFERENCES
1. J.P. Gauntlett, G.W. Gibbons, C.M. Hull, and
P.K. Townsend. BPS states of D=4 N=1
supersymmetry // Commun. Math. Phys. 2001,
v. 216, p. 431-459 (and refs. therein).
2. I. Bandos and J. Lukierski. Tensorial central
charges and new superparticle models with
fundamental spinor coordinates // Mod. Phys. Lett.
1999, v. A14, p. 1257-1272; I. Bandos, J. Lukierski
and D. Sorokin. Superparticle models with
tensorial central charges // Phys. Rev. 2000,
v. D61, p. 045002.
3. S. Fedoruk and V.G. Zima. Massive super-
particle with tensorial central charges //
Mod. Phys. Lett. 2000, v. A15, p. 2281-2296.
4. V.G. Zima and S.O. Fedoruk. Spinning
(super-) particle with a commuting index spinor //
JETP Lett. 1995, v. 61, p. 251-256.
5. V.G. Zima and S.O. Fedoruk. Weinberg
propagator of a free massive particle with an
arbitrary spin from the BFV-BRST path integral //
Class. Quantum Grav. 1999, v. 16, p. 3653-3671;
Representation of the propagator of a massive
spinning particle as a BFV-BRST path integral //
Phys. of Atomic Nucl. 2000, v. 63, p. 617-622.
6. F. Delduc, E. Ivanov and S. Krivonos. ¼
Partial breaking of global supersymmetry and new
superparticle actions // Nucl. Phys. 2000, v. B576,
p. 196-316.
7. S. Bellucci, A. Galajinsky, E. Ivanov and
S. Krivonos. Quantum mechanics of superparticle
with ¼ supersymmetry breaking. hep-th/0112075.
8. S. Fedoruk and V.G. Zima. Uniform twistor-
like formulation of massive and massless
superparticles with tensorial central charges //
Nucl. Phys. (Proc. Suppl.) 2001, v. B102&103,
p. 233-239.
9. J. Wess and J. Bagger, Supersymmetry and
Supergravity, 1983 (Princeton: Princeton
University Press).
10. R. Penrose. Twistor algebra // J. Math Phys.
1967, v. 8, p. 345-366; R. Penrose and
M.A.H. Mac Callum. Twistor theory: an approach
to the quantization of fields and space-time //
Phys. Rep. 1972, v. 6, p. 241-316.
11. A. Galperin, E. Ivanov, E. Kalizin,
V. Ogievetsky and E. Sokatchev. Unconstrained
N=2 matter, Yang-Mills and supergravity theories
in harmonic superspace // Class. Quantum Grav.
1984, v. 1, p. 469-498.
12. I.A. Bandos. Superparticle in Lorentz-
harmonic superspace // Sov. J. Nucl. Phys. 1990,
v. 51, p. 906-921; I.A. Bandos and
A.A. Zheltukhin. N=1 super- p -branes in twistor-
like Lorentz harmonic formulation //
Class. Quantum Grav. 1995, v. 12, p. 609-625.
13. V.G. Zima and S.O. Fedoruk. Covariant
quantization of the d=4 Brink-Schwarz
superparticle using Lorentz harmonics // Theor.
Math. Phys. 1995, v. 102, p. 305-322.
14. I.A. Bandos, J.A. deAzcarraga,
J.M. Izquerdo and J. Lukierski. BPS states in M-
theory and twistorial constituents // Phys. Rev. Lett.
2001, v. A14, p. 1257-1300.
64
TWISTORIAL SUPERPARTICLE
WITH TENSORIAL CENTRAL CHARGES
S.A. Fedoruk1, V.G. Zima2
1Ukrainian Engineering Pedagogical Academy, Kharkov, Ukraine
2Kharkov National University, Kharkov, Ukraine
|
| id | nasplib_isofts_kiev_ua-123456789-79424 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:11:39Z |
| publishDate | 2001 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Fedoruk, S.A. Zima, V.G. 2015-04-01T19:29:07Z 2015-04-01T19:29:07Z 2001 Twistorial superparticle with tensorial central charges / S.A. Fedoruk, V.G. Zima // Вопросы атомной науки и техники. — 2001. — № 6. — С. 60-64. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 11.15.-q, 11.17.+y, 02.40.+m, 11.30.Pb https://nasplib.isofts.kiev.ua/handle/123456789/79424 A twistorial formulation of the N=1 D=4 superparticle with tensorial central charges describing massive and massless cases in uniform manner is given. The twistors resolve energy-momentum vector whereas the tensorial central charges are written in term of spinor Lorentz harmonics. The model makes possible to describe states preserving all allowed fractions of target-space supersymmetry. The full analysis of the number of conserved supersymmetries in models with N=1 D=4 superalgebra with tensorial central charges has been carried out. This work was supported in part by INTAS Grant INTAS-2000-254 and by the Ukrainian National Found of Fundamental Researches under the Project № 02.07/383. We would like to thank I.A. Bandos, A. Frydryszak, E.A. Ivanov, S.O. Krivonos, J. Lukierski, A.J. Nurmagambetov and D.P. Sorokin for interest to the work and for many useful discussions. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Quantum field theory Twistorial superparticle with tensorial central charges Твисторная суперчастица с тензорными центральными зарядами Article published earlier |
| spellingShingle | Twistorial superparticle with tensorial central charges Fedoruk, S.A. Zima, V.G. Quantum field theory |
| title | Twistorial superparticle with tensorial central charges |
| title_alt | Твисторная суперчастица с тензорными центральными зарядами |
| title_full | Twistorial superparticle with tensorial central charges |
| title_fullStr | Twistorial superparticle with tensorial central charges |
| title_full_unstemmed | Twistorial superparticle with tensorial central charges |
| title_short | Twistorial superparticle with tensorial central charges |
| title_sort | twistorial superparticle with tensorial central charges |
| topic | Quantum field theory |
| topic_facet | Quantum field theory |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79424 |
| work_keys_str_mv | AT fedoruksa twistorialsuperparticlewithtensorialcentralcharges AT zimavg twistorialsuperparticlewithtensorialcentralcharges AT fedoruksa tvistornaâsuperčasticastenzornymicentralʹnymizarâdami AT zimavg tvistornaâsuperčasticastenzornymicentralʹnymizarâdami |