Noncommutativity and Partial Supersymmetry Breaking in Field Theory and its String Theoretic Origin

a collaboration between Hanover and Dubna / Tomsk / Moscow, Russia
duration: since 2002
researchers: De Castro, Gutschwager, Lechtenfeld, Kürkçüoglu, Popov, Quevedo, Schwerdtfeger, Thürigen;
                    Fedoruk, Ivanov, Ivanova, Krivonos, Polovnikov, Shcherbakov, Sorin, Sutulin, Zupnik;
                    Buchbinder, Galajinsky, Krykhtin, Lavrov, Perschin, Petrov, Pletnev, Reshetnyak, Samsonov; Domrin, Sergeev; Olshanetsky;
                    Delduc, Ferrara, Sokatchev
funding: DFG - RFFI (cooperation project) (travel), Heisenberg-Landau (travel), INTAS (travel), AvH (1 postdoc 07-08)
other projects

Abstract:

Noncommutative generalizations of field theory models appeared as a low-energy limit of the open bosonic string coupled to a constant background B-field. Studying various noncommutative field models and revealing their stringy origin constitute one of the mainstream directions in modern field theory. Via string compactifications on noncommutative internal spaces new possibilities appear for constructing phenomenologically viable string scenarios, perhaps including the Standard Model.

Before attempting to quantize noncommutative field theories, it is important to characterize the moduli space of their classical configurations. The generalization of solitons and instantons of various field models to the noncommutative realm has just begun. But much of our knowledge of conventional field theory still awaits a noncommutative counterpart. In particular, the methods and results of exactly solvable and supersymmetric field theories should be generalized on the noncommutative case. The formulation of supersymmetric models in noncommutative N=1 superspace has been recently given. It is an important and urgent problem to develop the appropriate superspace methods of quantizing supersymmetric noncommutative field theories.

The concept of the partial breaking of global supersymmetry (PBGS) can be taken as the primary guiding principle for deducing the worldvolume brane actions. Besides being manifestly invariant under the unbroken worldvolume supersymmetry, they automatically possess a nonlinearly realized part of the full original supersymmetry. It is tempting to apply the PBGS methods to analyze noncommutative phenomena in brane theories and their field theory descendants. One of the characteristic features of noncommutative field models is the breaking of Lorentz symmetry in the ambient (super)spaces. The spontaneous breaking of Lorentz symmetry is also inherent in the PBGS approach. It could happen that both effects have a common origin.

Dirac-Born-Infeld (DBI) actions and their supersymmetric extensions are closely related both with noncommutativity (Seiberg-Witten transform) and string theory (effective actions of massless excitations in the open string theory and worldvolume actions of Dp-branes). They naturally appear within the PBGS approach as the actions of the Goldstone vector supermultiplets. A proposal on possible structure of non-abelian bosonic Born-Infeld action was made recently. It makes sense to construct possible deformations of SYM equations perturbatively as a series in string parameter alpha. The general structure of this expansion beyond first orders is unknown. A closely related problem is to adapt the PBGS approach for deriving non-abelian DBI actions. An interesting unsolved problem is to find out a true (super)gravity analog of the DBI action. It could be relevant to the theory of closed strings.

Recently, a new formulation of superstring quantization was proposed by Berkovits. It uses so called pure spinors as auxiliary worldsheet variables and maintains a manifest spacetime supersymmetry. This approach was used for the calculation of scattering amplitudes for an arbitrary number of massless vectors and was shown to be equivalent to the Ramond-Neveu-Schwarz formulation. It could also be a tool to investigate the duality between strongly coupled gauge theories and supergravity/superstring theories on specific manifolds. A physical quantity that can be calculated using this scheme is the potential between static sources in gauge theory which on the string theory side corresponds to a partition function of the string with the end-points fixed at given Wilson loops. The structure of loop corrections to the tree-approximation value of this quantity is unknown. However, a general restriction on the possible form of such a potential was found, based on positivity properties of the euclidian version of gauge theory. Finding the exact form of the quantum corrections suffers from the absence of a covariant quantization scheme for the superstring. The pure-spinor quantization could be helpful in this respect.

The problems which are supposed to be solved within the project:

Investigation of string compactifications on noncommutative internal spaces. Studying phenomenological issues and stability properties of such string vacua.
Construction of noncommutative instantons and monopoles by the dressing method. Studying noncommutative solitons/branes in N=2 string field theory.
Quantum calculations of the effective actions in noncommutative extended supersymmetric field theories.
Derivation of branes and strings from the partial spontaneous breaking of supersymmetry as the guiding principle. Superfield analysis of the brane and string models with partially broken local supersymmetry, construction of stringy generalizations of the supergravity worldvolume actions.
Application of the harmonic-superspace approach for the off-shell description of quantum properties of extended supersymmetric gauge theories. Development of the quantum-supergraph method in the N=3 gauge theory and the construction of the N=3 Born-Infeld action in the framework of the harmonic superspace. Definition and analysis of noncommutative N=3 harmonic superspace and its higher N analogs.
Constructing (non)commutative, open and periodic Toda lattice hierarchies with extended supersymmetries and investigating relevance of their integrable structure for different low energy regimes and/or deformations of supersymmetric Yang-Mills theories.
Investigation of the noncommutative torus in the framework of integrable theories. Study of the role of the sin-algebra for hidden symmetries. Analysis of the Hitchin type elliptic systems.
Noncommutative deformation of the Seiberg-Witten equations for N=2 supersymmetric Yang-Mills theory in the IR limit. Constructing their solutions. Reducing the noncommutative Seiberg-Witten equations to noncommutative vortex equations.
Development of extended BRST covariant quantization in general coordinates. Generalizations of this method to noncommutative gauge theories.
Evaluation of stringy corrections to D=10 SYM using Berkovits' formulation of the superstring with pure spinors. Analysis of the low energy dynamics for the D=10 SYM theory using this covariant superstring formulation.
Covariant quantization of the superstring in AdS_5 times S^5. Calculation of quantum corrections to the static-sources potential in the framework of the AdS/CFT correspondence.
Construction of the N=1 superconformal sigma-model describing the RNS superstring in massive background fields.

Papers related to Hannover:

Sergey Fedoruk, Evgeny Ivanov and Olaf Lechtenfeld:
Nahm equation in N=4 mechanics with spin multiplet
arXiv:1204.4474 [hep-th] ()

Sergey Fedoruk, Evgeny Ivanov and Olaf Lechtenfeld:
Superconformal mechanics
arXiv:1112.1947 [hep-th] (J. Phys. A: Math. Theor. 45 (2012) 173001) (invited review article)

Peter Lavrov, Olaf Lechtenfeld and Alexander Reshetnyak:
Is soft breaking of BRST symmetry consistent?
arXiv:1108.4820 [hep-th] (JHEP 1110 (2011) 043)

Sergey Krivonos and Olaf Lechtenfeld:
Many-particle mechanics with D(2,1;alpha) superconformal symmetry
arXiv:1012.4639 [hep-th] (JHEP 1102 (2011) 042)

Olaf Lechtenfeld, Konrad Schwerdtfeger and Johannes Thürigen:
N=4 multi-particle mechanics, WDVV equation and roots
arXiv:1011.2207 [hep-th] (SIGMA 7 (2011) 023)

Sergey Krivonos, Olaf Lechtenfeld and Anton Sutulin:
N=4 supersymmetry and the BPST instanton
arXiv:1001.2659 [hep-th] (Phys. Rev. D 81 (2010) 085021)

Sergey Fedoruk, Evgeny Ivanov and Olaf Lechtenfeld:
New super Calogero models and OSp(4|2) superconformal mechanics
arXiv:1001.2536 [hep-th]
(Talk by E.I. at the XIII International Conference "Symmetry Methods in Physics", Dubna, Russia, 06-09 July 2009)

Sergey Fedoruk, Evgeny Ivanov and Olaf Lechtenfeld:
New D(2,1;alpha) mechanics with spin variables
arXiv:0912.3508 [hep-th] (JHEP 1004 (2010) 129)

I.L. Buchbinder, E.A. Ivanov, O. Lechtenfeld, N.G. Pletnev, I.B. Samsonov and B.M. Zupnik:
Quantum N=3, d=3 Chern-Simons matter theories in harmonic superspace
arXiv:0909.2970 [hep-th] (JHEP 0910 (2009) 075)

Tigran Hakobyan, Sergey Krivonos, Olaf Lechtenfeld and Armen Nersessian:
Hidden symmetries of integrable conformal mechanical systems
arXiv:0908.3290 [hep-th] (Phys. Lett. A 374 (2010) 801-806)

Olaf Lechtenfeld and Kirill Polovnikov:
A new class of solutions to the WDVV equation
arXiv:0907.2244 [hep-th] (Phys. Lett. A 374 (2010) 504-506)

Anton Galajinsky and Olaf Lechtenfeld:
Harmonic N=2 mechanics
arXiv:0907.2242 [hep-th] (Phys. Rev. D 80 (2009) 065012)

Sergey Krivonos and Olaf Lechtenfeld:
SU(2) reduction in N=4 supersymmetric mechanics
arXiv:0906.2469 [hep-th] (Phys. Rev. D 80 (2009) 045019)

Sergey Fedoruk, Evgeny Ivanov and Olaf Lechtenfeld:
OSp(4|2) superconformal mechanics
arXiv:0905.4951 [hep-th] (JHEP 0908 (2009) 081)

Sergey Krivonos, Olaf Lechtenfeld and Kirill Polovnikov:
N=4 superconformal n-particle mechanics via superspace
arXiv:0812.5062 [hep-th] (Nucl. Phys. B 817 [PM] (2009) 265-283)

Sergey Fedoruk, Evgeny Ivanov and Olaf Lechtenfeld:
Supersymmetric Calogero models by gauging
arXiv:0812.4276 [hep-th] (Phys. Rev. D 79 (2009) 105015)

I.L. Buchbinder, E.A. Ivanov, O. Lechtenfeld, N.G. Pletnev, I.B. Samsonov and B.M. Zupnik:
ABJM models in N=3 harmonic superspace
arXiv:0811.4774 [hep-th] (JHEP 0903 (2009) 096)

Olaf Lechtenfeld
WDVV solutions from orthocentric polytopes and Veselov systems
arXiv:0804.3245 [hep-th] (in: Problems of Modern Theoretical Physics, ed. V. Epp, Tomsk State Pedagogical University Press, 2008, pp. 256-265)

Ioseph L. Buchbinder, Olaf Lechtenfeld and Igor B. Samsonov
N=4 superparticle and super Yang-Mills theory in USp(4) harmonic superspace
arXiv:0804.3063 [hep-th] (Nucl. Phys. B 802 (2008) 208-246)

Anton Galajinsky, Olaf Lechtenfeld and Kirill Polovnikov:
N=4 mechanics, WDVV equations and roots
arXiv:0802.4386 [hep-th] (JHEP 0903 (2009) 113)

Ioseph L. Buchbinder and Igor B. Samsonov:
N=3 superparticle model
arXiv:0801.4907 [hep-th] ()

Stefano Bellucci, Sergey Krivonos, Olaf Lechtenfeld and Andrey Shcherbakov:
Superfield formulation of nonlinear N=4 supermultiplets
arXiv:0710.3832 [hep-th] (Phys. Rev. D 77 (2008) 045026)

I.L. Buchbinder, E.A. Ivanov, O. Lechtenfeld, I.B. Samsonov and B.M. Zupnik:
Gauge theory in deformed N=(1,1) superspace
arXiv:0709.3770 [hep-th] (Phys. Part. Nucl. 39 (2008) 759-797)

Francois Delduc, Olaf Lechtenfeld and Alexander Sorin:
N=2 supersymmetric unconstrained matrix GNLS hierarchies are consistent
arXiv:0708.1125 [nlin.SI] (Lett. Math. Phys. 84 (2008) 109-122)

Anton Galajinsky, Olaf Lechtenfeld and Kirill Polovnikov:
N=4 superconformal Calogero models
arXiv:0708.1075 [hep-th] (JHEP 0711 (2007) 008)
(also talk by O.L. at JINR workshop ``Supersymmetries and Quantum Symmetries'', Dubna, Russia, 30 July-04 Aug 2007; short version appears in the Proceedings)

Evgeny Ivanov, Olaf Lechtenfeld and Anton Sutulin:
Hierarchy of N=8 mechanics models
arXiv:0705.3064 [hep-th] (Nucl. Phys. B 790 [PM] (2008) 493-523)

I.L. Buchbinder, O. Lechtenfeld and I.B. Samsonov:
Vector-mutliplet effective action in the non-anticommutative charged hypermultiplet model
hep-th/0608048 (Nucl. Phys. B 758 (2006) 185-203)

Anton Galajinsky, Olaf Lechtenfeld and Kirill Polovnikov:
Calogero models and nonlocal conformal transformations
hep-th/0607215 (Phys. Lett. B 643 (2006) 221-227)

Yu. Chernikov, A.M. Levin, M. Olshanetsky and A.Zotov:
Elliptic Schlesinger system and Painleve VI
nlin.SI/0602043 ()

Alexandra De Castro, Evgeny Ivanov, Olaf Lechtenfeld and Leonardo Quevedo:
Non-singlet Q-deformations of N=2 gauge theories
hep-th/0512275
(Talk by A.D.C. at JINR workshop ``Supersymmetries and Quantum Symmetries'', Dubna, Russia, 27-31 July 2005;
Proceedings: SQS '05, pp. 116-121)

I. Buchbinder, E. Ivanov, O. Lechtenfeld, I. Samsonov and B. Zupnik:
Renormalizability of non-anticommutative N=(1,1) theories with singlet deformation
hep-th/0511234 (Nucl. Phys. B 740 (2006) 358-385)

Alexandra De Castro, Evgeny Ivanov, Olaf Lechtenfeld and Leonardo Quevedo:
Non-singlet Q-deformation of the N=(1,1) vector multiplet in harmonic superspace
hep-th/0510013 (Nucl. Phys. B 747 (2006) 1-24)

Andrei V. Domrin, Olaf Lechtenfeld and Stefan Petersen:
Sigma-model solitons in the noncommutative plane: construction and stability analysis
hep-th/0412001 (JHEP 0503 (2005) 045)

Evgenyi Ivanov, Olaf Lechtenfeld and Boris Zupnik:
Non-anticommutative deformation of N=(1,1) hypermultiplets
hep-th/0408146 (Nucl. Phys. B 707 (2005) 69-86)

Stefano Bellucci, Evgeny Ivanov, Sergey Krivonos and Olaf Lechtenfeld:
ABC of N=8, d=1 supermultiplets
hep-th/0406015 (Nucl. Phys. B 699 (2004) 226-252)

Alexandra De Castro, Leonardo Quevedo and Alvaro Restuccia:
N=2 super-Born-Infeld from partially broken N=3 supersymmetry in d=4
hep-th/0405062 (JHEP 0406 (2004) 055)

Sergio Ferrara, Evgeny Ivanov, Olaf Lechtenfeld, Emery Sokatchev and Boris Zupnik:
Non-anticommutative chiral singlet deformation of N=(1,1) gauge theory
hep-th/0405049 (Nucl. Phys. B 704 (2005) 154-180)

Evgeny Ivanov, Olaf Lechtenfeld and Boris Zupnik:
Non-anticommutative N=(1,1) Euclidean superspace
hep-th/0402062
(Talk by E.I. at JINR workshop ``Supersymmetries and Quantum Symmetries'', Dubna, Russia, 24-29 July 2003;
Proceedings 2004: SQS'03, pp. )

Olaf Lechtenfeld and Alexander S. Sorin:
A note on fermionic flows of the N=(1|1) supersymmetric Toda lattice hierarchy
nlin.SI/0401029 (J. Nonlinear Math. Phys. 11 (2004) 294-296)

Stefano Bellucci, Evgenyi Ivanov, Sergey Krivonos and Olaf Lechtenfeld:
N=8 superconformal mechanics
hep-th/0312322 (Nucl. Phys. B 684 (2004) 321-350)

Evgenyi Ivanov, Sergey Krivonos and Olaf Lechtenfeld:
N=4, d=1 supermultiplets from nonlinear realizations of D(2,1;alpha)
hep-th/0310299 (Class. Quantum Grav. 21 (2004) 1031-1050)

Evgenyi Ivanov, Olaf Lechtenfeld and Boris Zupnik:
Nilpotent deformations of N=2 superspace
hep-th/0308012 (JHEP 0402 (2004) 012)

Evgenyi Ivanov and Olaf Lechtenfeld:
N=4 supersymmetric mechanics in harmonic superspace
hep-th/0307111 (JHEP 0309 (2003) 073)

Alexander D. Popov, Armen G. Sergeev and Martin Wolf:
Seiberg-Witten monopole equations on noncommutative R⁴
hep-th/0304263 (J. Math. Phys. 44 (2003) 4527-4554)

Evgenyi Ivanov, Sergey Krivonos and Olaf Lechtenfeld:
New variant of N=4 superconformal mechanics
hep-th/0212303 (JHEP 0303 (2003) 014)