scholarly journals A note on ensemble holography for rational tori

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Joris Raeymaekers
Keyword(s):  
Path Integral ◽  
Weighted Average ◽  
Gravity Theory ◽  
Ensemble Average ◽  
Chiral Algebra ◽  
Boundary Path ◽  
Modular Invariants ◽  
Holographic Duality ◽  
Chern Simons

Abstract We study simple examples of ensemble-averaged holography in free compact boson CFTs with rational values of the radius squared. These well-known rational CFTs have an extended chiral algebra generated by three currents. We consider the modular average of the vacuum character in these theories, which results in a weighted average over all modular invariants. In the simplest case, when the chiral algebra is primitive (in a sense we explain), the weights in this ensemble average are all equal. In the non-primitive case the ensemble weights are governed by a semigroup structure on the space of modular invariants.These observations can be viewed as evidence for a holographic duality between the ensemble of CFTs and an exotic gravity theory based on a compact U(1) × U(1) Chern-Simons action. In the bulk description, the extended chiral algebra arises from soliton sectors, and including these in the path integral on thermal AdS3 leads to the vacuum character of the chiral algebra. We also comment on wormhole-like contributions to the multi-boundary path integral.

scholarly journals Brane gravity in 4D from Chern–Simons gravity theory

2020 ◽  
Vol 80 (6) ◽  
Author(s):  
R. Díaz ◽  
F. Gómez ◽  
M. Pinilla ◽  
P. Salgado
Keyword(s):  
Gravity Theory ◽  
Chern Simons ◽  
Brane Gravity

A THREE-DIMENSIONAL COVARIANT APPROACH TO MONODROMY (SKEIN RELATIONS) IN CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (32) ◽  
pp. 2747-2751 ◽  
Author(s):  
B. BRODA
Keyword(s):  
Integral Representation ◽  
Path Integral ◽  
Wilson Loop ◽  
Three Dimensional ◽  
Simons Theory ◽  
Monodromy Operator ◽  
Covariant Approach ◽  
Path Integral Representation ◽  
Chern Simons ◽  
Chern Simons Theory

A genuinely three-dimensional covariant approach to the monodromy operator (skein relations) in the context of Chern-Simons theory is proposed. A holomorphic path-integral representation for the holonomy operator (Wilson loop) and for the non-abelian Stokes theorem is used.

scholarly journals EFFECTS OF CHERN–SIMONS CORRECTIONS ON CONSERVED QUANTITIES OF RELATIVISTIC FLUID

2010 ◽  
Vol 25 (31) ◽  
pp. 2655-2666
Author(s):  
KOHKICHI KONNO ◽  
TOYOKI MATSUYAMA ◽  
SATOSHI TANDA
Keyword(s):  
Fluid Flow ◽  
Modified Gravity ◽  
Gravity Theory ◽  
Conserved Quantities ◽  
Maxwell Theory ◽  
Relativistic Fluid ◽  
Modified Gravity Theory ◽  
Chern Simons

We consider relativistic fluid flow under Chern–Simons modified Maxwell theory and under Chern–Simons modified gravity theory. We take account of the effects of Chern–Simons corrections on the quantities of fluid flow that is conserved without the Chern–Simons corrections. We find that the conservations of several quantities are generally broken by the Chern–Simons corrections.

FRACTIONAL STATISTICS INDUCED BY GAUGE FIELDS

1991 ◽  
Vol 06 (05) ◽  
pp. 391-398 ◽  
Author(s):  
ASHOK CHATTERJEE ◽  
V.V. SREEDHAR
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Path Integral ◽  
Simple Proof ◽  
Scalar Particle ◽  
Gauge Fields ◽  
Fractional Statistics ◽  
Chern Simons

An explicit extension of Polyakov’s analysis of a scalar particle coupled to an Abelian Chern-Simons gauge theory to the case of two particles and arbitrary values of the coupling is given. A simple proof of the emergence of fractional statistics induced by the gauge field follows within the path-integral framework.

scholarly journals Exceptional Chern-Simons-Matter dualities

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Clay Cordova ◽  
Po-Shen Hsin ◽  
Kantaro Ohmori
Keyword(s):  
Gauge Theory ◽  
Topological Field Theories ◽  
Time Reversal ◽  
Three Dimensional ◽  
Field Theories ◽  
Chiral Algebra ◽  
Gauge Groups ◽  
Topological Field ◽  
Conformal Embeddings ◽  
Chern Simons

We use conformal embeddings involving exceptional affine Kac-Moody algebras to derive new dualities of three-dimensional topological field theories. These generalize the familiar level-rank duality of Chern-Simons theories based on classical gauge groups to the setting of exceptional gauge groups. For instance, one duality sequence we discuss is (E_{N})_{1}\leftrightarrow SU(9-N)_{-1}(EN)1↔SU(9−N)−1. Others such as SO(3)_{8}\leftrightarrow PSU(3)_{-6},SO(3)8↔PSU(3)−6, are dualities among theories with classical gauge groups that arise due to their embedding into an exceptional chiral algebra. We apply these equivalences between topological field theories to conjecture new boson-boson Chern-Simons-matter dualities. We also use them to determine candidate phase diagrams of time-reversal invariant G_{2}G2 gauge theory coupled to either an adjoint fermion, or two fundamental fermions.

NON-ABELIAN GAUGE THEORY FOR CHERN–SIMONS PATH INTEGRAL ON R3

2012 ◽  
Vol 21 (04) ◽  
pp. 1250039 ◽  
Author(s):  
ADRIAN P. C. LIM
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Path Integral ◽  
Wilson Loop ◽  
Wiener Measure ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Chern Simons

In a prequel to this article, we used abstract Wiener measure to define the Chern–Simons path integral over ℝ3. In this sequel, we compute the Wilson Loop observable for the non-abelian gauge group and compare with current knot literature.

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