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 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 Poincaré series, 3d gravity and averages of rational CFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Viraj Meruliya ◽  
Sunil Mukhi ◽  
Palash Singh
Keyword(s):  
Poincaré Series ◽  
Simons Theory ◽  
Partition Functions ◽  
Moody Algebra ◽  
Modular Invariant ◽  
Poincare Series ◽  
Single Genus ◽  
3D Gravity ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We investigate the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)k WZW models provide unitary examples for which the Poincaré series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT’s sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU(N)1 and SU(3)k, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions — the latter corresponding to analogues of 3-manifold “wormholes” — such that the expected average is correctly reproduced.

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 Exact Computations in Topological Abelian Chern-Simons and BF Theories

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Philippe Mathieu
Keyword(s):  
Simons Theory ◽  
Partition Functions ◽  
Topological Invariants ◽  
Deligne Cohomology ◽  
Functional Integrals ◽  
Fibre Bundles ◽  
Bf Theory ◽  
Chern Simons ◽  
Chern Simons Theory

We introduce Deligne cohomology that classifies U1 fibre bundles over 3 manifolds endowed with connections. We show how the structure of Deligne cohomology classes provides a way to perform exact (nonperturbative) computations in U1 Chern-Simons theory (BF theory, resp.) at the level of functional integrals. The partition functions (and observables) of these theories are strongly related to topological invariants well known to the mathematicians.

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 Higher-derivative supergravity, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Nikolay Bobev ◽  
Anthony M. Charles ◽  
Dongmin Gang ◽  
Kiril Hristov ◽  
Valentin Reys
Keyword(s):  
Black Holes ◽  
Three Dimensional ◽  
Simons Theory ◽  
Partition Functions ◽  
Infinite Class ◽  
Gauge Groups ◽  
Higher Derivative ◽  
Hyperbolic Three Manifolds ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $$ \mathrm{\mathcal{R}} $$ ℛ . Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-N expansion of supersymmetric partition functions for an infinite class of three-dimensional $$ \mathcal{N} $$ N = 2 SCFTs of class $$ \mathrm{\mathcal{R}} $$ ℛ . We also determine the leading correction to the Bekenstein-Hawking entropy of asymptotically AdS4 black holes arising from wrapped M5-branes. In addition, we propose and test some conjectures about the perturbative partition function of Chern-Simons theory with complexified ADE gauge groups on closed hyperbolic three-manifolds.

scholarly journals Wilson loops in superconformal Chern-Simons theory and fundamental strings in Anti-de Sitter supergravity dual

2009 ◽  
Vol 2009 (03) ◽  
pp. 127-127 ◽  
Author(s):  
Soo-Jong Rey ◽  
Takao Suyama ◽  
Satoshi Yamaguchi
Keyword(s):  
Simons Theory ◽  
Wilson Loops ◽  
De Sitter ◽  
Chern Simons ◽  
Chern Simons Theory

CHERN-SIMONS THEORY AND KAUFFMAN POLYNOMIALS

1990 ◽  
Vol 05 (06) ◽  
pp. 1165-1195 ◽  
Author(s):  
YONG-SHI WU ◽  
KENGO YAMAGISHI
Keyword(s):  
Lie Algebras ◽  
Simons Theory ◽  
Wilson Loops ◽  
Expectation Values ◽  
Simple Lie Algebras ◽  
Link Invariants ◽  
Chern Simons ◽  
Knots And Links ◽  
Chern Simons Theory

We report on a study of the expectation values of Wilson loops in D=3 Chern-Simons theory. The general skein relations (of higher orders) are derived for these expectation values. We show that the skein relations for the Wilson loops carrying the fundamental representations of the simple Lie algebras SO(n) and Sp(n) are sufficient to determine invariants for all knots and links and that the resulting link invariants agree with Kauffman polynomials. The polynomial for an unknotted circle is identified to the formal characters of the fundamental representations of these Lie algebras.

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