scholarly journals SUPER-LAX OPERATOR EMBEDDED IN SELF-DUAL SUPERSYMMETRIC YANG-MILLS THEORY

1996 ◽  
Vol 11 (30) ◽  
pp. 2417-2426 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Integrable Models ◽  
Three Dimensions ◽  
Superstring Theory ◽  
Lax Equation ◽  
Yang Mills ◽  
Guiding Principle ◽  
Lax Operator ◽  
Geometrical Relationship

We show that the super-Lax operator for N=1 supersymmetric Kadomtsev-Petviashvili (SKP) equation of Manin and Radul in three dimensions can be embedded into recently developed self-dual supersymmetric Yang-Mills theory in 2+2 dimensions, based on general features of its underlying super-Lax equation. The whole hierarchy of the SKP equations of Manin and Radul is generated by geometrical superfield equations of self-dual supersymmetric Yang-Mills theory. The differential geometrical relationship in superspace between the embedding principle of the super-Lax operator and its associated super-Sato equation is clarified. This result provides a good guiding principle for the embedding of other integrable subsystems in the super-Lax equation into the four-dimensional self-dual supersymmetric Yang-Mills theory, which is the consistent background for N=2 superstring theory, and potentially generates other unknown supersymmetric integrable models in lower dimensions.

N=2 SUPERSTRING THEORY GENERATES SUPERSYMMETRIC CHERN-SIMONS THEORIES

1994 ◽  
Vol 09 (35) ◽  
pp. 3255-3266 ◽  
Author(s):  
HITOSHI NISHINO
Keyword(s):  
Integrable Models ◽  
Three Dimensions ◽  
Superstring Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Fundamental Significance ◽  
Background Fields ◽  
Chern Simons

We show that the action of self-dual supersymmetric Yang-Mills theory in four dimensions, which describes the consistent massless background fields for N=2 superstring, generates the actions for N=1 and N=2 supersymmetric non-Abelian Chern-Simons theories in three dimensions after some dimensional reductions. Since the latters play important roles for supersymmetric integrable models, this result indicates the fundamental significance of the N=2 superstring theory controlling (possibly all) supersymmetric integrable models in lower dimensions.

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 Exact extended supersymmetry on a lattice: Twisted N=4 super-Yang–Mills in three dimensions

2008 ◽  
Vol 798 (1-2) ◽  
pp. 168-183 ◽  
Author(s):  
Alessandro D'Adda ◽  
Issaku Kanamori ◽  
Noboru Kawamoto ◽  
Kazuhiro Nagata
Keyword(s):  
Extended Supersymmetry ◽  
Three Dimensions ◽  
Yang Mills

scholarly journals On the Mini-Superambitwistor Space and𝒩=8Super-Yang-Mills Theory

2009 ◽  
Vol 2009 ◽  
pp. 1-27 ◽  
Author(s):  
Christian Sämann
Keyword(s):  
Dimensional Reduction ◽  
Three Dimensions ◽  
Third Order ◽  
Yang Mills

We construct a new supertwistor space suited for establishing a Penrose-Ward transform between certain bundles over this space and solutions to the𝒩=8super-Yang-Mills equations in three dimensions. This mini-superambitwistor space is obtained by dimensional reduction of the superambitwistor space, the standard superextension of the ambitwistor space. We discuss in detail the construction of this space and its geometry before presenting the Penrose-Ward transform. We also comment on a further such transform for purely bosonic Yang-Mills-Higgs theory in three dimensions by considering third-order formal “subneighborhoods” of a miniambitwistor space.

scholarly journals The Yang-Mills heat equation with finite action in three dimensions

2022 ◽  
Vol 275 (1349) ◽  
Author(s):  
Leonard Gross
Keyword(s):  
Heat Equation ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Three Dimensions ◽  
Dimensional Manifold ◽  
Uniqueness Of Solutions ◽  
Reconstruction Procedure ◽  
Content Type ◽  
Yang Mills ◽  
Gauge Functions

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R 3 \mathbb {R}^3 and over a bounded open convex set in R 3 \mathbb {R}^3 . The initial data is taken to lie in the Sobolev space of order one half, which is the critical Sobolev index for this equation over a three dimensional manifold. The existence is proven by solving first an augmented, strictly parabolic equation and then gauge transforming the solution to a solution of the Yang-Mills heat equation itself. The gauge functions needed to carry out this procedure lie in the critical gauge group of Sobolev regularity three halves, which is a complete topological group in a natural metric but is not a Hilbert Lie group. The nature of this group must be understood in order to carry out the reconstruction procedure. Solutions to the Yang-Mills heat equation are shown to be strong solutions modulo these gauge functions. Energy inequalities and Neumann domination inequalities are used to establish needed initial behavior properties of solutions to the augmented equation.

scholarly journals Evidence for weak-coupling holography from the gauge/gravity correspondence for Dp-branes

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Yasuhiro Sekino
Keyword(s):  
Gauge Theory ◽  
Free Field ◽  
Scalar Fields ◽  
Superstring Theory ◽  
Spatial Direction ◽  
Strongly Coupled ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Brane Solution ◽  
Gauge Gravity

Abstract Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D$p$-branes ($0\le p\le 4$), namely, the duality between the $(p+1)$D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D$p$-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for $p\neq 3$. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form ${\rm Tr}(Z^J)$, where $Z$ is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into $J$ bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

ALGEBRAIC STUDY ON THE POISSON STRUCTURE OF LAX OPERATOR OF B AND C TYPE AND SUPER LAX OPERATOR.

1992 ◽  
Vol 07 (supp01a) ◽  
pp. 405-418
Author(s):  
KAORU IKEDA
Keyword(s):  
Poisson Structure ◽  
Algebraic Structure ◽  
Lax Equation ◽  
Lax Operator

The Poisson structure of Lax operator of B and C type and super Lax operator which has odd parity are studied. The algebraic structure of Poisson structure as a background of Lax equation is thrown light on.

CANONICAL BÄCKLUND TRANSFORMATION FOR A DISCRETE INTEGRABLE CHAIN AND ITS ASSOCIATED PROPERTIES

2003 ◽  
Vol 18 (16) ◽  
pp. 1127-1139
Author(s):  
A. GHOSE CHOUDHURY ◽  
BARUN KHANRA ◽  
A. ROY CHOWDHURY
Keyword(s):  
Poisson Structure ◽  
Algebraic Structure ◽  
Bäcklund Transformation ◽  
Inverse Transformation ◽  
Strict Sense ◽  
Backlund Transformation ◽  
Lax Equation ◽  
R Matrix ◽  
Lax Operator ◽  
Time Part

The concept of a canonical Bäcklund transformation as laid down by Sklyanin is extended to a discrete integral chain, with a Poisson structure which is not canonical in the strict sense. The transformation is induced by an auxiliary Lax operator with a classical r-matrix which is similar in its algebraic structure to that of the original Lax operator governing the dynamics of the chain. Moreover, the transformation can be obtained from a suitable generating function. It is also shown how successive transformations can be composed to construct a new transformation. Finally an inverse transformation is also constructed. The compatibility of the transformation with the "time" part of the Lax equation is explicitly demonstrated. It is also shown that the Bianchi theorem of permutability holds good.

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