scholarly journals Path integral contour deformations for observables in SU(N) gauge theory

2021 ◽  
Vol 103 (9) ◽  
Author(s):  
William Detmold ◽  
Gurtej Kanwar ◽  
Henry Lamm ◽  
Michael L. Wagman ◽  
Neill C. Warrington
Keyword(s):  
Gauge Theory ◽  
Path Integral ◽  
Integral Contour

scholarly journals Eigenbranes in Jackiw-Teitelboim gravity

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Andreas Blommaert ◽  
Thomas G. Mertens ◽  
Henri Verschelde
Keyword(s):  
Finite Volume ◽  
Chaotic System ◽  
Path Integral ◽  
Hermitian Matrices ◽  
The Matrix ◽  
Integral Contour

Abstract It was proven recently that JT gravity can be defined as an ensemble of L × L Hermitian matrices. We point out that the eigenvalues of the matrix correspond in JT gravity to FZZT-type boundaries on which spacetimes can end. We then investigate an ensemble of matrices with 1 ≪ N ≪ L eigenvalues held fixed. This corresponds to a version of JT gravity which includes N FZZT type boundaries in the path integral contour and which is found to emulate a discrete quantum chaotic system. In particular this version of JT gravity can capture the behavior of finite-volume holographic correlators at late times, including erratic oscillations.

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 Hamiltonian, Path Integral and BRST Formulations of the Restricted Gauge Theory of <i>QCD<sub>2</sub></i>

2018 ◽  
Vol 09 (14) ◽  
pp. 2355-2369
Author(s):  
Usha Kulshreshtha ◽  
Daya Shankar Kulshreshtha ◽  
James P. Vary
Keyword(s):  
Gauge Theory ◽  
Path Integral ◽  
Hamiltonian Path

scholarly journals TOWARDS THE LOCALIZATION OF SUSY GAUGE THEORY ON A CURVED SPACE

2012 ◽  
Vol 27 (06) ◽  
pp. 1250029 ◽  
Author(s):  
KOICHI NAGASAKI ◽  
SATOSHI YAMAGUCHI
Keyword(s):  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Path Integral ◽  
General Class ◽  
Positive Definite ◽  
Curved Space ◽  
Yang Mills ◽  
Curved Spaces ◽  
Supersymmetric Gauge ◽  
Exact Term

We consider an [Formula: see text] supersymmetric gauge theory on a curved space. We try to generalize Pestun's localization calculation on the four-sphere to a more general class of curved spaces. We calculated the Q-exact term to localize the path-integral, and when it becomes positive-definite, we obtain a configuration where the path-integral localizes. We also evaluate the super-Yang–Mills action in this configuration.

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.

scholarly journals Measure of the path integral in lattice gauge theory

2005 ◽  
Vol 71 (7) ◽  
Author(s):  
F. Paradis ◽  
H. Kröger ◽  
X. Q. Luo ◽  
K. J. M. Moriarty
Keyword(s):  
Gauge Theory ◽  
Path Integral ◽  
Lattice Gauge Theory ◽  
Lattice Gauge

scholarly journals On Gauge Invariance of the Bosonic Measure in Chiral Gauge Theories

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 283
Author(s):  
Gabriel de Lima e Silva ◽  
Thalis José Girardi ◽  
Sebastião Alves Dias
Keyword(s):  
Hilbert Space ◽  
Gauge Theory ◽  
Path Integral ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Direct Calculation ◽  
Identity Operator ◽  
Anomaly Cancellation ◽  
Gauge Anomaly ◽  
General Gauge

Gauge invariance of the measure associated with the gauge field is usually taken for granted, in a general gauge theory. We furnish a proof of this invariance, within Fujikawa’s approach. To stress the importance of this fact, we briefly review gauge anomaly cancellation as a consequence of gauge invariance of the bosonic measure and compare this cancellation to usual results from algebraic renormalization, showing that there are no potential inconsistencies. Then, using a path integral argument, we show that a possible Jacobian for the gauge transformation has to be the identity operator, in the physical Hilbert space. We extend the argument to the complete Hilbert space by a direct calculation.

scholarly journals Path integral contour deformations for noisy observables

2020 ◽  
Vol 102 (1) ◽  
Author(s):  
William Detmold ◽  
Gurtej Kanwar ◽  
Michael L. Wagman ◽  
Neill C. Warrington
Keyword(s):  
Path Integral ◽  
Integral Contour

scholarly journals Classification of out-of-time-order correlators

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Felix Haehl ◽  
R. Loganayagam ◽  
Prithvi Narayan ◽  
Mukund Rangamani
Keyword(s):  
Correlation Function ◽  
Path Integral ◽  
Correlation Functions ◽  
General Structure ◽  
Natural Generalization ◽  
Functional Integrals ◽  
Time Order ◽  
Integral Contour ◽  
Point Correlation

The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator. These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions). We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours. Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions. We provide explicit illustration for low point correlators (n\leq 4n≤4) to exemplify the general statements.

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