scholarly journals Holographic and localization calculations of boundary F for $$ \mathcal{N} $$ = 4 SUSY Yang-Mills theory

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Mark Van Raamsdonk ◽  
Chris Waddell
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Partition Function ◽  
Boundary Conditions ◽  
Half Space ◽  
Scale Invariance ◽  
Entanglement Entropy ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Renormalization Group Flows

Abstract $$ \mathcal{N} $$ N = 4 Supersymmetric Yang-Mills (SYM) theory can be defined on a half-space with a variety of boundary conditions preserving scale invariance and half of the original supersymmetry; more general theories with the same symmetry can be obtained by coupling to a 3D SCFT at the boundary. Each of these theories is characterized by a quantity called “boundary F”, conjectured to decrease under boundary renormalization group flows. In this paper, we calculate boundary F for U(N) $$ \mathcal{N} $$ N = 4 SYM theory with the most general half-supersymmetric boundary conditions arising from string theory constructions with D3-branes ending on collections of D5-branes and/or NS5-branes. We first perform the calculation holographically by evaluating the entanglement entropy for a half-ball centered on the boundary using the Ryu-Takayanagi formula in the dual type IIB supergravity solutions. For boundary conditions associated with D3-branes ending on D5 branes only or NS5-branes only, we also calculate boundary F exactly by evaluating the hemisphere partition function using supersymmetric localization. The leading terms at large N in the supergravity and localization results agree exactly as a function of the t’ Hooft coupling λ.

scholarly journals $$ T\overline{T} $$-deformation of q-Yang-Mills theory

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Leonardo Santilli ◽  
Richard J. Szabo ◽  
Miguel Tierz
Keyword(s):  
Phase Transition ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Line Bundles ◽  
Boltzmann Entropy ◽  
Third Order ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We derive the $$ T\overline{T} $$ T T ¯ -perturbed version of two-dimensional q-deformed Yang-Mills theory on an arbitrary Riemann surface by coupling the unperturbed theory in the first order formalism to Jackiw-Teitelboim gravity. We show that the $$ T\overline{T} $$ T T ¯ -deformation results in a breakdown of the connection with a Chern-Simons theory on a Seifert manifold, and of the large N factorization into chiral and anti-chiral sectors. For the U(N) gauge theory on the sphere, we show that the large N phase transition persists, and that it is of third order and induced by instantons. The effect of the $$ T\overline{T} $$ T T ¯ -deformation is to decrease the critical value of the ’t Hooft coupling, and also to extend the class of line bundles for which the phase transition occurs. The same results are shown to hold for (q, t)-deformed Yang-Mills theory. We also explicitly evaluate the entanglement entropy in the large N limit of Yang-Mills theory, showing that the $$ T\overline{T} $$ T T ¯ -deformation decreases the contribution of the Boltzmann entropy.

scholarly journals Renormalization-group flows and charge transmutation in string theory

2006 ◽  
Vol 54 (5-6) ◽  
pp. 453-461 ◽  
Author(s):  
D. Orlando ◽  
P.M. Petropoulos ◽  
K. Sfetsos
Keyword(s):  
Renormalization Group ◽  
String Theory ◽  
Renormalization Group Flows

scholarly journals TWO-DIMENSIONAL YANG-MILLS THEORIES ARE STRING THEORIES

1993 ◽  
Vol 08 (23) ◽  
pp. 2223-2235 ◽  
Author(s):  
STEPHEN G. NACULICH ◽  
HAROLD A. RIGGS ◽  
HOWARD J. SCHNITZER
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Arbitrary Number ◽  
Closed String ◽  
Two Dimensional ◽  
Branched Covers ◽  
Yang Mills ◽  
String Worldsheet ◽  
String Theories

We show that two-dimensional SO (N) and Sp (N) Yang-Mills theories without fermions can be interpreted as closed string theories. The terms in the 1/N expansion of the partition function on an orientable or nonorientable manifold ℳ can be associated with maps from a string worldsheet onto ℳ. These maps are unbranched and branched covers of ℳ with an arbitrary number of infinitesimal worldsheet cross-caps mapped to points in ℳ. These string theories differ from SU (N) Yang-Mills string theory in that they involve odd powers of 1/N and require both orientable and nonorientable worldsheets.

scholarly journals Effects of non-conformal boundary on entanglement entropy

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Andrew Loveridge
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Conformal Field Theory ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Conformal Symmetry ◽  
Entanglement Entropy ◽  
Mixed Boundary Conditions ◽  
De Sitter ◽  
Conformal Field

Abstract Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but “mixed” boundary conditions which interpolate linearly between them can break conformal symmetry and generate interesting Renormalization Group flows even when a theory is free, providing soluble models with nontrivial scale dependence. We compute the (Rindler) entanglement entropy for a free scalar field with mixed boundary conditions in half Minkowski space and in Anti-de Sitter space. In the latter case we also compute an additional geometric contribution, which according to a recent proposal then collectively give the 1/N corrections to the entanglement entropy of the conformal field theory dual. We obtain some perturbatively exact results in both cases which illustrate monotonic interpolation between ultraviolet and infrared fixed points. This is consistent with recent work on the irreversibility of renormalization group, allowing some assessment of the aforementioned proposal for holographic entanglement entropy and illustrating the generalization of the g-theorem for boundary conformal field theory.

scholarly journals RENORMALIZATION GROUP FLOWS IN THE DEFORMED ADS/CFT CORRESPONDENCE

2001 ◽  
Vol 16 (11) ◽  
pp. 2027-2033
Author(s):  
NICK EVANS
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Moduli Space ◽  
Radial Direction ◽  
Renormalization Group Flow ◽  
Yang Mills ◽  
Infra Red ◽  
Renormalization Group Flows ◽  
Group Flow

In the AdS/CFT correspondence motion in the radial direction of the AdS space is identified with renormalization group flow in the field theory. For the N=4 Yang-Mills theory this motion is trivial. More interesting examples of renormalization group flow occur when the N=4 theory is deformed. Aspects of the flows are discussed for the N=4 theory on its moduli space, and deformed to N=2 in the infra-red within the context of 5d SUGRA. 10d lifts and brane probing are crucial tools for linking the spacetime backgrounds to the dual field theory.

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 Deconstructing little strings with $\mathcal{N}=1$ gauge theories on ellipsoids

2018 ◽  
Vol 4 (6) ◽  
Author(s):  
Joseph Hayling ◽  
Rodolfo Panerai ◽  
Constantinos Papageorgakis
Keyword(s):  
String Theory ◽  
Partition Function ◽  
Analytic Continuation ◽  
Gauge Theories ◽  
Partition Functions ◽  
Yang Mills ◽  
The Relationship

A formula was recently proposed for the perturbative partition function of certain \mathcal N=1𝒩=1 gauge theories on the round four-sphere, using an analytic-continuation argument in the number of dimensions. These partition functions are not currently accessible via the usual supersymmetric-localisation technique. We provide a natural refinement of this result to the case of the ellipsoid. We then use it to write down the perturbative partition function of an \mathcal N=1𝒩=1 toroidal-quiver theory (a double orbifold of \mathcal N=4𝒩=4 super Yang–Mills) and show that, in the deconstruction limit, it reproduces the zero-winding contributions to the BPS partition function of (1,1) Little String Theory wrapping an emergent torus. We therefore successfully test both the expressions for the \mathcal N=1𝒩=1 partition functions, as well as the relationship between the toroidal-quiver theory and Little String Theory through dimensional deconstruction.

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