Scientific biography of Stanley Mandelstam: 1981–2016

2017 ◽  
Vol 32 (12) ◽  
pp. 1740011
Author(s):  
Nathan Berkovits
Keyword(s):  
Light Cone ◽  
Scientific Biography ◽  
Superstring Theory ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Memorial Volume ◽  
Super Yang Mills Theory

In this contribution to the memorial volume, I will review Stanley Mandelstam’s work after 1980 and concentrate on his powerful application of light-cone gauge methods in super-Yang–Mills theory and superstring theory.

scholarly journals New modular invariants in $$ \mathcal{N} $$ = 4 Super-Yang-Mills theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Shai M. Chester ◽  
Michael B. Green ◽  
Silviu S. Pufu ◽  
Yifan Wang ◽  
Congkao Wen
Keyword(s):  
Eisenstein Series ◽  
Mass Parameter ◽  
Flat Space ◽  
Superstring Theory ◽  
Modular Invariant ◽  
Yang Mills ◽  
Laplace Eigenvalue ◽  
Modular Invariants ◽  
Tensor Multiplet ◽  
Super Yang Mills Theory

Abstract We study modular invariants arising in the four-point functions of the stress tensor multiplet operators of the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory, in the limit where N is taken to be large while the complexified Yang-Mills coupling τ is held fixed. The specific four-point functions we consider are integrated correlators obtained by taking various combinations of four derivatives of the squashed sphere partition function of the $$ \mathcal{N} $$ N = 2∗ theory with respect to the squashing parameter b and mass parameter m, evaluated at the values b = 1 and m = 0 that correspond to the $$ \mathcal{N} $$ N = 4 theory on a round sphere. At each order in the 1/N expansion, these fourth derivatives are modular invariant functions of (τ,$$ \overline{\tau} $$ τ ¯ ). We present evidence that at half-integer orders in 1/N , these modular invariants are linear combinations of non-holomorphic Eisenstein series, while at integer orders in 1/N, they are certain “generalized Eisenstein series” which satisfy inhomogeneous Laplace eigenvalue equations on the hyperbolic plane. These results reproduce known features of the low-energy expansion of the four-graviton amplitude in type IIB superstring theory in ten-dimensional flat space and have interesting implications for the structure of the analogous expansion in AdS5× S5.

scholarly journals Flat self-dual gravity

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Kirill Krasnov ◽  
Evgeny Skvortsov
Keyword(s):  
Light Cone ◽  
Space Time ◽  
Kinetic Term ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Covariant Action ◽  
Chiral Interaction ◽  
Double Copy

Abstract We construct a new covariant action for “flat” self-dual gravity in four space-time dimensions. The action has just one term, but when expanded around an appropriate background gives rise to a kinetic term and a cubic interaction. Upon imposing the light-cone gauge, the action reproduces the expected chiral interaction of Siegel. The new action is in many ways analogous to the known covariant action for self-dual Yang-Mills theory. There is also a sense in which the new self-dual gravity action exhibits the double copy of self-dual Yang-Mills structure.

scholarly journals Quantum integrability in (super) Yang–Mills theory on the light-cone

2004 ◽  
Vol 594 (3-4) ◽  
pp. 385-401 ◽  
Author(s):  
A.V. Belitsky ◽  
S.É. Derkachov ◽  
G.P. Korchemsky ◽  
A.N. Manashov
Keyword(s):  
Light Cone ◽  
Yang Mills ◽  
Quantum Integrability ◽  
Super Yang Mills Theory

scholarly journals EXACT SOLUTIONS TO THE TWO-DIMENSIONAL BF AND YANG–MILLS THEORIES IN THE LIGHT-CONE GAUGE

2002 ◽  
Vol 17 (11) ◽  
pp. 1491-1502 ◽  
Author(s):  
MITSUO ABE ◽  
NOBORU NAKANISHI
Keyword(s):  
Exact Solution ◽  
Quantum Gravity ◽  
Light Cone ◽  
Lagrangian Density ◽  
Critical Dimension ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Bf Theory ◽  
Conformal Gauge

It is shown that the BRS (= Becchi–Rouet–Stora)-formulated two-dimensional BF theory in the light-cone gauge (coupled with chiral Dirac fields) is solved very easily in the Heisenberg picture. The structure of the exact solution is very similar to that of the BRS-formulated two-dimensional quantum gravity in the conformal gauge. In particular, the BRS Noether charge has anomaly. Based on this fact, a criticism is made on the reasoning of Kato and Ogawa, who derived the critical dimension D=26 of string theory on the basis of the anomaly of the BRS Noether charge. By adding the [Formula: see text] term to the BF-theory Lagrangian density, the exact solution to the two-dimensional Yang–Mills theory is also obtained.

scholarly journals DUALITY AND COSMOLOGICAL COMPACTIFICATION OF SUPERSTRINGS WITH UNBROKEN SUPERSYMMETRY

1999 ◽  
Vol 14 (07) ◽  
pp. 1035-1047
Author(s):  
H. K. JASSAL ◽  
A. MUKHERJEE ◽  
R. P. SAXENA
Keyword(s):  
Scale Factor ◽  
Initial Singularity ◽  
Superstring Theory ◽  
Duality Transformation ◽  
Yang Mills ◽  
Consistency Conditions ◽  
Cosmological Solutions ◽  
Super Yang Mills Theory

The cosmological compactification of D=10, N=1 supergravity–super-Yang–Mills theory obtained from superstring theory is studied. The constraint of unbroken N=1 supersymmetry is imposed. A duality transformation is performed on the resulting consistency conditions. The original equations as well as the transformed equations are solved numerically to obtain new configurations with a nontrivial scale factor and a dynamical dilaton. It is shown that various classes of solutions are possible, which include cosmological solutions with no initial singularity.

scholarly journals Improved results forN=(2,2)super Yang-Mills theory using supersymmetric discrete light-cone quantization

2004 ◽  
Vol 70 (4) ◽  
Author(s):  
Motomichi Harada ◽  
John R. Hiller ◽  
Stephen Pinsky ◽  
Nathan Salwen
Keyword(s):  
Light Cone ◽  
Yang Mills ◽  
Light Cone Quantization ◽  
Super Yang Mills Theory

The light-cone gauge

1986 ◽  
Vol 64 (5) ◽  
pp. 624-632 ◽  
Author(s):  
H. C. Lee
Keyword(s):  
Quantum Chromodynamics ◽  
Quantum Electrodynamics ◽  
Light Cone ◽  
Field Theories ◽  
Special Role ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Light Cone Gauge ◽  
Yang Mills ◽  
Kaluza Klein

Some aspects of recent development in the light-cone gauge and its special role in quantum-field theories are reviewed. Topics discussed include the two- and four-component formulations of the light-cone gauge, Slavnov–Taylor and Becchi– Rouet–Stora identities, quantum electrodynamics, quantum chromodynamics, renormalization of Yang–Mills theory and supersymmetric theory, gravity, and the quantum-induced compactification of Kaluza–Klein theories in the light-cone gauge.

One-loop renormalization of the Yang-Mills theory with Dirac fermions in the light-cone gauge

1986 ◽  
Vol 33 (2) ◽  
pp. 617-618 ◽  
Author(s):  
A. Bassetto ◽  
M. Dalbosco ◽  
R. Soldati
Keyword(s):  
Light Cone ◽  
Dirac Fermions ◽  
Light Cone Gauge ◽  
Yang Mills

scholarly journals Dual expansions of super Yang–Mills theory via IIB superstring theory

2000 ◽  
Vol 585 (3) ◽  
pp. 517-553 ◽  
Author(s):  
Gordon Chalmers ◽  
Johanna Erdmenger
Keyword(s):  
Superstring Theory ◽  
Yang Mills ◽  
Super Yang Mills Theory
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