2D SIGMA MODEL APPROACH TO 4D INSTANTONS

1992 ◽  
Vol 07 (07) ◽  
pp. 1415-1447 ◽  
Author(s):  
Q-HAN PARK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Sigma Model ◽  
Gauge Groups ◽  
Yang Mills ◽  
Infinite Dimensional ◽  
Conformal Field ◽  
Toda Field Theory ◽  
Model Approach

4D self-dual theories are proposed to generalize 2D conformal field theory. We identify 4D self-dual gravity as well as self-dual Yang-Mills theory with 2D sigma models valued in infinite-dimensional gauge groups. It is shown that these models possess infinite-dimensional symmetries with associated algebras—“CP1 extensions” of respective gauge algebras of 2D sigma models—which generalize the Kac-Moody algebra as well as W∞. We address various issues concerning 2D sigma models, twistors and sheaf cohomology. An attempt to connect 4D self-dual theories with 2D conformal field theory is made through sl (∞) Toda field theory.

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

Integrability in 2D fields theory/sigma-models

2019 ◽  
pp. 248-318
Author(s):  
Sergei L. Lukyanov ◽  
Alexander B. Zamolodchikov
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field ◽  
Zero Curvature ◽  
Basic Facts ◽  
Linear Sigma Models ◽  
General Aspects

This is a two-part course about the integrability of two-dimensional non-linear sigma models (2D NLSM). In the first part general aspects of classical integrability are discussed, based on the O(3) and O(4) sigma-models and the field theories related to them. The second part is devoted to the quantum 2D NLSM. Among the topics considered are: basic facts of conformal field theory, zero-curvature representations, integrals of motion, one-loop renormalizability of 2D NLSM, integrable structures in the so-called cigar and sausage models, and their RG flows. The text contains a large number of exercises of varying levels of difficulty.

scholarly journals CAUSAL TRANSFORMATION OF GÖDEL-TYPE SPACETIMES IN CONFORMAL FIELD THEORY

2010 ◽  
Vol 25 (34) ◽  
pp. 2873-2884 ◽  
Author(s):  
PAWEL GUSIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Closed Timelike Curves ◽  
Conformal Field

The Gödel-type metrics are considered as backgrounds of the sigma-models. In the conformal field theory such backgrounds are deformed by the exactly marginal operators. We examine, how the closed timelike curves (CTCs) transform under such deformations.

scholarly journals Strongly γ -Deformed N=4 Supersymmetric Yang-Mills Theory as an Integrable Conformal Field Theory

2018 ◽  
Vol 120 (11) ◽  
Author(s):  
David Grabner ◽  
Nikolay Gromov ◽  
Vladimir Kazakov ◽  
Gregory Korchemsky
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Yang Mills ◽  
Conformal Field

scholarly journals ON SIX-DIMENSIONAL FUNDAMENTAL SUPERSTRINGS AS HOLOGRAMS

2009 ◽  
Vol 24 (01) ◽  
pp. 141-159 ◽  
Author(s):  
MOHSEN ALISHAHIHA ◽  
SUBIR MUKHOPADHYAY
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Model ◽  
Two Dimensional ◽  
World Sheet ◽  
Black String ◽  
Light Cone Gauge ◽  
Conformal Field ◽  
The World ◽  
Horizon Geometry

In this paper we discuss a possible holographic dual of the two-dimensional conformal field theory associated with the world-sheet of a macroscopic superstring in a compactification on a four-torus. We assume that the near-horizon geometry of the black string has symmetries of AdS 3×S3×T4 and construct a sigma model in the bulk. Analyzing the symmetries of the bulk theory and comparing them with those of the CFT in a special light-cone gauge, we find agreement between global symmetries. Due to nonstandard gauge realization it is not clear how affine symmetries can be realized.

scholarly journals O(N) sigma model as a three-dimensional conformal field theory

1995 ◽  
Vol 438 (3) ◽  
pp. 491-521 ◽  
Author(s):  
S. Guruswamy ◽  
S.G. Rajeev ◽  
P. Vitale
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Model ◽  
Three Dimensional ◽  
Conformal Field
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