scholarly journals The SCI of $$ \mathcal{N} $$ = 4 USp(2Nc) and SO(Nc) SYM as a matrix integral

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Antonio Amariti ◽  
Marco Fazzi ◽  
Alessia Segati
Keyword(s):  
Gauge Group ◽  
Simons Theory ◽  
Legendre Transform ◽  
Three Sphere ◽  
Matrix Integral ◽  
The Matrix ◽  
Point Solution ◽  
Chern Simons ◽  
Orthogonal Case ◽  
Chern Simons Theory

Abstract We study the superconformal index of 4d $$ \mathcal{N} $$ N = 4 USp(2Nc) and SO(Nc) SYM from a matrix model perspective. We focus on the Cardy-like limit of the index. Both in the symplectic and orthogonal case the index is dominated by a saddle point solution which we identify, reducing the calculation to a matrix integral of a pure Chern-Simons theory on the three-sphere. We further compute the subleading logarithmic corrections, which are of the order of the center of the gauge group. In the USp(2Nc) case we also study other subleading saddles of the matrix integral. Finally we discuss the case of the Leigh-Strassler fixed point with SU(Nc) gauge group, and we compute the entropy of the dual black hole from the Legendre transform of the entropy function.

scholarly journals Exact results and Schur expansions in quiver Chern-Simons-matter theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Leonardo Santilli ◽  
Miguel Tierz
Keyword(s):  
Simons Theory ◽  
Partition Functions ◽  
Wilson Loops ◽  
Model Formulation ◽  
Schur Polynomials ◽  
Three Sphere ◽  
The Matrix ◽  
The Masses ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters tj = −e2πmj , where mj are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.

scholarly journals What Chern–Simons theory assigns to a point

2017 ◽  
Vol 114 (51) ◽  
pp. 13418-13423 ◽  
Author(s):  
André G. Henriques
Keyword(s):  
Gauge Group ◽  
Von Neumann Algebras ◽  
Mathematical Object ◽  
Loop Group ◽  
Simons Theory ◽  
Fusion Product ◽  
Positive Energy ◽  
Von Neumann ◽  
Chern Simons ◽  
Chern Simons Theory

We answer the questions, “What does Chern–Simons theory assign to a point?” and “What kind of mathematical object does Chern–Simons theory assign to a point?” Our answer to the first question is representations of the based loop group. More precisely, we identify a certain class of projective unitary representations of the based loop group 𝛀G. We define the fusion product of such representations, and we prove that, modulo certain conjectures, the Drinfel’d center of that representation category of 𝛀G is equivalent to the category of positive energy representations of the free loop group LG.† The abovementioned conjectures are known to hold when the gauge group is abelian or of type A1. Our answer to the second question is bicommutant categories. The latter are higher categorical analogs of von Neumann algebras: They are tensor categories that are equivalent to their bicommutant inside Bim(R), the category of bimodules over a hyperfinite 𝐼𝐼𝐼1 factor. We prove that, modulo certain conjectures, the category of representations of the based loop group is a bicommutant category. The relevant conjectures are known to hold when the gauge group is abelian or of type An.

scholarly journals On partition functions of refined Chern-Simons theories on S3

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
M.Y. Avetisyan ◽  
R.L. Mkrtchyan
Keyword(s):  
Partition Function ◽  
Gauge Group ◽  
Topological Strings ◽  
Simons Theory ◽  
Partition Functions ◽  
Coupling Constant ◽  
Sine Functions ◽  
Chern Simons ◽  
Arbitrary Gauge ◽  
Chern Simons Theory

Abstract We present a new expression for the partition function of the refined Chern-Simons theory on S3 with an arbitrary gauge group, which is explicitly equal to 1 when the coupling constant is zero. Using this form of the partition function we show that the previously known Krefl-Schwarz representation of the partition function of the refined Chern-Simons theory on S3 can be generalized to all simply laced algebras.For all non-simply laced gauge algebras, we derive similar representations of that partition function, which makes it possible to transform it into a product of multiple sine functions aiming at the further establishment of duality with the refined topological strings.

scholarly journals Chern-Simons theory with finite gauge group

1993 ◽  
Vol 156 (3) ◽  
pp. 435-472 ◽  
Author(s):  
Daniel S. Freed ◽  
Frank Quinn
Keyword(s):  
Gauge Group ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

scholarly journals Symmetries of abelian Chern-Simons theories and arithmetic

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Diego Delmastro ◽  
Jaume Gomis
Keyword(s):  
Time Reversal ◽  
Quadratic Residue ◽  
Complete Characterization ◽  
Simons Theory ◽  
Prime Factorization ◽  
Residue Modulo ◽  
The Matrix ◽  
Quantum Symmetries ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We determine the unitary and anti-unitary Lagrangian and quantum symmetries of arbitrary abelian Chern-Simons theories. The symmetries depend sensitively on the arithmetic properties (e.g. prime factorization) of the matrix of Chern-Simons levels, revealing interesting connections with number theory. We give a complete characterization of the symmetries of abelian topological field theories and along the way find many theories that are non-trivially time-reversal invariant by virtue of a quantum symmetry, including U(1)k Chern-Simons theory and (ℤk)ℓ gauge theories. For example, we prove that U(1)k Chern-Simons theory is time-reversal invariant if and only if −1 is a quadratic residue modulo k, which happens if and only if all the prime factors of k are Pythagorean (i.e., of the form 4n + 1), or Pythagorean with a single additional factor of 2. Many distinct non-abelian finite symmetry groups are found.

scholarly journals On resolutions of cosmological singularities in higher-spin gravity

2019 ◽  
Vol 28 (15) ◽  
pp. 1950168
Author(s):  
Benjamin Burrington ◽  
Leopoldo A. Pando Zayas ◽  
Nicholas Rombes
Keyword(s):  
Gauge Group ◽  
Three Dimensional ◽  
Big Bang ◽  
Simons Theory ◽  
Gauge Potential ◽  
Cosmological Singularity ◽  
Gauge Transformations ◽  
Higher Spin ◽  
Chern Simons ◽  
Chern Simons Theory

We study the resolution of certain cosmological singularity in the context of higher-spin three-dimensional gravity. We consider gravity coupled to a spin-3 field realized as Chern–Simons theory with gauge group [Formula: see text]. In this context, we elaborate and extend a singularity resolution scheme proposed by Krishnan and Roy. We discuss the resolution of a big bang singularity in the case of gravity coupled to a spin-4 field realized as Chern–Simons theory with gauge group [Formula: see text]. In all these cases, we show the existence of gauge transformations that do not change the holonomy of the Chern–Simons gauge potential and lead to metrics without the initial singularity. We argue that such transformations always exist in the context of gravity coupled to a spin-[Formula: see text] field when described by Chern–Simons with gauge group [Formula: see text].

scholarly journals Exact results for perturbative Chern–Simons theory with complex gauge group

2009 ◽  
Vol 3 (2) ◽  
pp. 363-443 ◽  
Author(s):  
Tudor Dimofte ◽  
Sergei Gukov ◽  
Jonatan Lenells ◽  
Don Zagier
Keyword(s):  
Gauge Group ◽  
Simons Theory ◽  
Exact Results ◽  
Chern Simons ◽  
Chern Simons Theory
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