scholarly journals The topologically twisted index of $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Junho Hong
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Partition Function ◽  
Laplace Transform ◽  
Bethe Ansatz ◽  
Inverse Laplace Transform ◽  
Black String ◽  
Canonical Partition Function ◽  
Yang Mills ◽  
3D Black Hole

Abstract We investigate the large-N asymptotics of the topologically twisted index of $$ \mathcal{N} $$ N = 4 SU(N) Super-Yang-Mills (SYM) theory on T2 × S2 and provide its holographic interpretation based on the black hole Farey tail [1]. In the field theory side, we use the Bethe-Ansatz (BA) formula, which gives the twisted index of $$ \mathcal{N} $$ N = 4 SYM theory as a discrete sum over Bethe vacua, to compute the large-N asymptotics of the twisted index. In a dual $$ \mathcal{N} $$ N = 2 gauged STU model, we construct a family of 5d extremal solutions uplifted from the 3d black hole Farey tail, and compute the regularized on-shell actions. The gravitational partition function given in terms of these regularized on-shell actions is then compared with a canonical partition function derived from the twisted index by the inverse Laplace transform, in the large-N limit. This extends the previous microstate counting of an AdS5 black string by the twisted index and thereby improves holographic understanding of the twisted index.

THE FIRST DONALDSON INVARIANT AS THE WINDING NUMBER OF A NICOLAI MAP

1988 ◽  
Vol 03 (17) ◽  
pp. 1647-1650 ◽  
Author(s):  
P. MANSFIELD
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Partition Function ◽  
Relativistic Quantum ◽  
Quantum Field ◽  
Winding Number ◽  
Relativistic Quantum Field Theory ◽  
Yang Mills ◽  
Stochastic Map

We show that the first Donaldson invariant expressed by Witten as the partition function of a relativistic quantum field theory can be interpreted as the winding number of the stochastic map introduced by Nicolai in the context of supersymmetric Yang-Mills theories.

scholarly journals $O(\bar{d}, \bar{d})$ TRANSFORMATIONS AND 3D BLACK HOLE

1993 ◽  
Vol 08 (22) ◽  
pp. 2045-2052 ◽  
Author(s):  
ABBAS ALI ◽  
ALOK KUMAR
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
String Theory ◽  
Black Hole Solution ◽  
Three Dimensional ◽  
Black String ◽  
Rotating Black Hole ◽  
3D Black Hole

We generalize the results of a previous paper by one of the authors to show a relationship among a class of string solutions through [Formula: see text] transformations. The results are applied to a rotating black hole solution of three-dimensional general relativity discussed recently. We extend the black hole solution to string theory and show its connection with the three-dimensional black string with nonzero momentum through an [Formula: see text] transformation of the above type.

scholarly journals COHOMOLOGICAL FIELD THEORY APPROACH TO MATRIX STRINGS

1999 ◽  
Vol 14 (25) ◽  
pp. 3979-4002 ◽  
Author(s):  
FUMIHIKO SUGINO
Keyword(s):  
Field Theory ◽  
String Theory ◽  
Partition Function ◽  
Three Dimensional ◽  
Exact Result ◽  
Theory Approach ◽  
Two Dimensional ◽  
Yang Mills ◽  
Infrared Limit ◽  
Cohomological Field Theory

In this paper we consider IIA and IIB matrix string theories which are defined by two-dimensional and three-dimensional super Yang–Mills theory with the maximal supersymmetry, respectively. We exactly compute the partition function of both of the theories by mapping to a cohomological field theory. Our result for the IIA matrix string theory coincides with the result obtained in the infrared limit by Kostov and Vanhove, and thus gives a proof of the exact quasiclassics conjectured by them. Further, our result for the IIB matrix string theory coincides with the exact result of IKKT model by Moore, Nekrasov and Shatashvili. It may be an evidence of the equivalence between the two distinct IIB matrix models arising from different roots.

scholarly journals SL(3, ℤ) Modularity and New Cardy limits of the $$ \mathcal{N} $$ = 4 superconformal index

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Vishnu Jejjala ◽  
Yang Lei ◽  
Sam van Leuven ◽  
Wei Li
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Black Hole ◽  
Parameter Family ◽  
Similar Form ◽  
Four Dimensions ◽  
Yang Mills ◽  
Superconformal Index ◽  
Super Yang Mills Theory

Abstract The entropy of 1/16-th BPS AdS5 black holes can be microscopically accounted for by the superconformal index of the $$ \mathcal{N} $$ N = 4 super-Yang-Mills theory. One way to compute this is through a Cardy-like limit of a formula for the index obtained in [1] using the “S-transformation” of the elliptic Γ function. In this paper, we derive more general SL(3, ℤ) modular properties of the elliptic Γ function. We then use these properties to obtain a three integer parameter family of generalized Cardy-like limits of the $$ \mathcal{N} $$ N = 4 superconformal index. From these limits, we obtain entropy formulae that have a similar form as that of the original AdS5 black hole, up to an overall rescaling of the entropy. We interpret this both on the field theory and the gravitational side. Finally, we comment on how our work suggests a generalization of the Farey tail to four dimensions.

Quantum gravity

1979 ◽  
Vol 368 (1732) ◽  
pp. 33-36
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
General Relativity ◽  
Black Hole ◽  
Quantum Theory ◽  
Asymptotic Freedom ◽  
Quantum Field ◽  
Yang Mills ◽  
Black Hole Background ◽  
New Ideas

The nature of the search for a quantum theory of gravity has undergone significant changes over the last few years. This is partly because the success of renormalized Yang-Mills gauge theory has stimulated interest in quantum field theory leading to a number of new ideas (for example instantons, solitons, monopoles, asymptotic freedom) which, focusing as they do on non-perturbative aspects, are potentially of considerable importance in a gravitational context. There has also been the development of supersymmetry and the associated supergravity theories for which the prognosis for quantization is brighter than normal General Relativity. Finally, a major impact was made by Hawking’s (1975) discovery of the thermal radiation produced when a quantum field propagates in a black hole background. This leads to a remarkable synthesis of thermodynamics, quantum theory and general relativity whose significance for physics has still not yet been fully explored. Traditionally, the methods for quantizing the gravitational field have been divided into ‘canonical’ and ‘covariant’ (Isham et al. 1975). A number of years ago the main attack on the canonical front was the quantization of the classical constraints

scholarly journals Black-hole–black-string phase transitions in thermal (1 + 1)-dimensional supersymmetric Yang–Mills theory on a circle

2004 ◽  
Vol 21 (22) ◽  
pp. 5169-5191 ◽  
Author(s):  
Ofer Aharony ◽  
Joseph Marsano ◽  
Shiraz Minwalla ◽  
Toby Wiseman
Keyword(s):  
Black Hole ◽  
Phase Transitions ◽  
Black String ◽  
Yang Mills

scholarly journals On a path integral representation of the Nekrasov instanton partition function and its Nekrasov–Shatashvili limit

2014 ◽  
Vol 92 (3) ◽  
pp. 267-270 ◽  
Author(s):  
Franco Ferrari ◽  
Marcin Piątek
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Path Integral ◽  
Equation Of Motion ◽  
Field Theories ◽  
Integral Expression ◽  
Path Integral Representation ◽  
Yang Mills ◽  
Fundamental Matter ◽  
Mills Field

In this work we study the Nekrasov–Shatashvili limit of the Nekrasov instanton partition function of Yang–Mills field theories with 𝒩 = 2 supersymmetry and gauge group SU(N). The theories are coupled with fundamental matter. A path integral expression of the full instanton partition function is derived. It is checked that in the Nekrasov–Shatashvili (thermodynamic) limit the action of the field theory obtained in this way reproduces exactly the equation of motion used in the saddle-point calculations.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

Sign in / Sign up

Export Citation Format

Share Document