N=2 Extended Fermionic Strings and Self-Dual Field Theories

duration: 1993-2000
researchers: Bischoff, Galajinsky, Hippmann, Jünemann, Ketov, Lechtenfeld, Marquart, Niemeyer, Spendig, Stroetmann, Unkmeir; Chalmers, Devchand, Ivanova, Parkes, Popov, Siegel
funding: DFG (1 PhD 10/95-02/00), Volkswagen foundation (sabbatical research), DAAD
other projects

Abstract:

Critical strings with (2,2) extended world-sheet supersymmetry are perhaps the only exactly solvable four-dimensional string theories, providing a consistent quantum theory of self-dual gravity and/or self-dual Yang-Mills theory. This hope derives from the observation that the spacetime background of signature (2,2) leaves no room for perturbative transverse string excitations and only a massless spectrum remains. Apparently, the critical N=2 string is a very special point particle in disguise, presumably described by a topological theory. In fact, consistency of duality with the absence of massive poles requires the vanishing of all string scattering amplitudes beyond the three-point function. In particular, the crucial vanishing of the four-point function is tied to the peculiar kinematics in 2+2 dimensions. This is as simple as a string theory can get.

In 1990, Ooguri and Vafa computed the tree-level amplitudes with up to four legs of the single massless physical field degree of freedom present in the critical N=2 string. The resulting (tree-level) effective spacetime dynamics was identified as that of self-dual gravity and of self-dual Yang-Mills theory for the cases of closed and open N=2 strings, respectively. More precisely, a massless scalar excitation of the open or closed N=2 spinning string satisfies the Leznov resp. the (second) Plebanski equation of motion and may therefore be identified classically with the single-helicity field degree of freedom in either self-dual field theory. The dynamics is such that all tree-level scattering amplitudes for Leznov and Plebanski scalars vanish beyond the three-point functions, a fact that is consistent with (old-fashioned) duality only because N=2 strings do not possess any further (massive) excitations! Beyond tree-level, a modular anomaly explains the discrepancy between the string loop amplitudes (which vanish) and the maximally helicity-violating Yang-Mills amplitudes (which do not).

In 1992, Siegel showed that N=2 strings are partially gauge-fixed versions of N=4 strings, the latter allegedly supporting maximal spacetime supersymmetry. In 1994, Berkovits and Vafa managed to embed the closed N=2 string into a topologically twisted N=4 string and introduced variables parametrizing the choices of complex structures in the 4d spacetime. Since self-dual structures in four dimensions are believed to unify all integrable systems in two and three dimensions, N=2 strings also teach us about the quantization of integrable models.

In this project, it was achieved to

analyze all possible twistings of N=2 strings
classify all possible GSO projections
outline the path-integral quantization including the loop measure
clarify the role of the R symmetry of N=2 world-sheet supergravity, the spectral flow of the N=2 superconformal algebra and the world-sheet Maxwell instantons
demonstrate that the world-sheet Maxwell instantons shift the parametrization from the Yang to the Leznov gauge for self-dual Yang-Mills
complete the analysis of physical states by computing the (relative) BRST cohomology (for many picture and ghost sectors and mass levels)
use BRST cohomology to classify the global symmetries and exploit their Ward identities
exhibit the space-time significance of the picture degeneracy phenomenon
uncover the hidden non-local symmetries of N=2 strings and their relation with SDYM and SDG hierarchy of integrable equations
prove the integrability of the covariant string field equations of motion
investigate the coupling of self-dual Yang-Mills to self-dual gravity and its stringy extensions
compute all N=2 string scattering amplitudes (including mixed open/closed) for all instanton sectors, up to and including one loop
compare with the maximally helicity violating amplitudes of ordinary Yang-Mills + gravity at tree and one-loop level, display a modular anomaly
construct space-time supersymmetric extensions (of the self-dual particle and string)
couple the open N=2 string to D branes and constant background B-fields and extract noncommutative selfdual Yang-Mills in the Seiberg-Witten limit

Papers:

Stefano Bellucci, Anton Galajinsky and Olaf Lechtenfeld:
A heterotic N=2 string with space-time supersymmetry
hep-th/0103049 (Nucl. Phys. B 609 (2001) 410-428)

Olaf Lechtenfeld, Alexander D. Popov and Bernd Spendig:
Open N=2 strings in a B-field background and noncommutative self-dual Yang-Mills
hep-th/0012200 (Phys. Lett. B 507 (2001) 317-326)

Olaf Lechtenfeld and Alexander D. Popov:
On the integrability of covariant field theory for the open N=2 string
hep-th/0009144 (Phys. Lett. B 494 (2000) 148-154)

Tatiana A. Ivanova and Olaf Lechtenfeld:
Hidden symmetries of the open N=2 string
hep-th/0007049 (Int. J. Mod. Phys. A 16 (2001) 303-329)

Gordon Chalmers, Olaf Lechtenfeld and Bernd Niemeyer:
N=2 quantum string scattering
hep-th/0007020 (Nucl. Phys. B 591 (2000) 1-38)

Olaf Lechtenfeld:
Mathematics and physics of N=2 strings
hep-th/9912281
(Talk at JINR workshop ``Supersymmetries and Quantum Symmetries'', Dubna, Russia, 27-31 July 1999;
Proceedings 2000: SQS'99, pp. 79-89)

Olaf Lechtenfeld and Alexander D. Popov:
Closed N=2 strings: picture-changing, hidden symmetries and SDG hierarchy
hep-th/9912154 (Int. J. Mod. Phys. A 15 (2000) 4191-4237)

Klaus Jünemann and Olaf Lechtenfeld:
Ward identities and the vanishing theorem for loop amplitudes of the closed N=2 string
hep-th/9912016 (Phys. Lett. B 474 (2000) 58-66)

Anton Galajinsky and Olaf Lechtenfeld:
Towards a stringy extension of self-dual super Yang-Mills
hep-th/9903149 (Phys. Lett. B 460 (1999) 288-294)

Klaus Jünemann, Olaf Lechtenfeld and Alexander D. Popov:
Non-local symmetries of the closed N=2 string
hep-th/9901164 (Nucl. Phys. B548 (1999) 449-474)

Chandrashekar Devchand and Olaf Lechtenfeld:
String-induced Yang-Mills coupling to self-dual gravity
hep-th/9808053 (Nucl. Phys. B 539 (1999) 309-328)

Chandrashekar Devchand and Olaf Lechtenfeld:
On the self-dual geometry of N=2 strings
hep-th/9801117
(Talk given at the 31st International Ahrenshoop Symposium on the Theory of Elementary Particles in Buckow, Germany, 2-6 September 1997, at the International Conference ``Methods in Field Theory'' in Stara Lesna, Slovakia, 22-26 September 1997, and the String Workshop in Wittenberg, Germany, 14-15 November, 1997)

Klaus Jünemann and Olaf Lechtenfeld:
Chiral BRST cohomology of the N=2 string at arbitrary ghost and picture number
hep-th/9712182 (Comm. Math. Phys. 203 (1999) 53)

Chandrashekar Devchand and Olaf Lechtenfeld:
Extended self-dual Yang-Mills from the N=2 string
hep-th/9712043 (Nucl. Phys. B 516 (1998) 255)

Sergei Ketov:
Do the critical (2,2) strings know about a supergravity in 2+10 dimensions ?
hep-th/9710086
(Talk at the XII International Congress of Mathematical Physics, 13-19 July, 1997, in Brisbane, Australia, and the 2nd International Conference on Quantum Field Theory and Gravity, July 29 - August 2, 1997, in Tomsk, Russia)

Olaf Lechtenfeld and Warren Siegel:
N=2 worldsheet instantons yield cubic self-dual Yang-Mills
hep-th/9704076 (Phys. Lett. B 405 (1997) 49)

Jan Bischoff and Olaf Lechtenfeld:
Path-integral quantization of the (2,2) string
hep-th/9612218 (Int. J. Mod. Phys. A 12 (1997) 4933)

Sergei Ketov:
Self-duality and F theory
hep-th/9612171
(Talk at the 4th Nordic Meeting `Supersymmetric Field and String Theories', Göteborg, September 1996, and at the `Mitteldeutsche' Workshop, Wittenberg, November 1996)

Sergei Ketov:
Mixed (open/closed) N=(2,2) string theory as an integrable deformation of self-duality
hep-th/9612170 (Phys. Lett. B 395 (1997) 48)

Sergei Ketov:
The OSp(32|1) versus OSp(8|2) supersymmetric M-brane action from self-dual (2,2) strings
hep-th/9609004 (Mod. Phys. Lett. A 11 (1996) 2369)

Jan Bischoff and Olaf Lechtenfeld:
Restoring reality for the self-dual N=2 string
hep-th/9608196 (Phys. Lett. B 390 (1997) 153)

Jan Bischoff:
Moduli und Amplituden des N=2 Strings
ITP-UH-14/96 (PhD Thesis)

Olaf Lechtenfeld:
The self-dual critical N=2 string
hep-th/9607106 (p.348, Dubna preprint JINR E2-96-369)
(Talk at X Int. Conf. `Problems of Quantum Field Theory', Alushta, Crimea, May 1996)

Sergei Ketov:
From N=2 strings to F&M theory
hep-th/9606142 (Nucl. Phys. B (Proc. Suppl.) 52A (1997) 335)
(Talk at the Int'l Workshop `Integrable Models and Strings', Garbsen, Germany, June 1996)

Sergei Ketov:
One-loop finiteness of the four-dimensional Donaldson-Nair-Schiff non-linear sigma-model
hep-th/9604141 (Phys. Lett. B 383 (1996) 390)

Olaf Lechtenfeld:
Integration measure and spectral flow in the critical N=2 string
hep-th/9512189 (Nucl. Phys. B (Proc. Suppl.) 49 (1996) 51)
(Talk at 29th Int. Ahrenshoop Symposium on Elem. Particle Theory, Buckow, Germany, 1995)

Sergei V. Ketov:
N=2 string loops and spectral flow
hep-th/9510005
(Talk at Int. Workshop on Strings, ICTP, Trieste, Italy, 1995)

Sergei V. Ketov:
On N=4 strings
(p.285, Proceedings)
(Talk at Int. Conf. "Strings '95", USC, Los Angeles, USA, 1995)

Olaf Lechtenfeld:
On the BRST cohomology of N=2 strings
hep-th/9508100 (p.309, Proceedings)
(Talk at Int. Conf. "Strings '95", USC, Los Angeles, USA, 1995)

Sergei V. Ketov and Olaf Lechtenfeld:
The string measure and spectral flow of critical N=2 strings
hep-th/9503232 (Phys. Lett. B 353 (1995) 463)

Olaf Lechtenfeld:
From N=2 fermionic strings to superstrings?
hep-th/9412242 (p.16, DESY preprint 95-027)
(Talk at 28th Int. Ahrenshoop Symp. on Elem. Particle Theory, Wendisch-Rietz, Germany, 1994)

Jan Bischoff, Sergei V. Ketov and Olaf Lechtenfeld:
The GSO projection, BRST cohomology and picture-changing in N=2 string theory
hep-th/9406101 (Nucl. Phys. B438 (1995) 373)

Sergei V. Ketov, Olaf Lechtenfeld and Andrew J. Parkes:
Twisting the N=2 string
hep-th/9312150 (Phys. Rev. D51 (1995) 2872)

Sergei V. Ketov:
Space-time supersymmetry of extended fermionic strings in 2+2 dimensions
hep-th/9302091 (Class. Quant. Grav. 10 (1993) 1689)