scholarly journals Averaging over Narain moduli space

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Alexander Maloney ◽  
Edward Witten
Keyword(s):  
Einstein Gravity ◽  
Two Dimensions ◽  
Three Dimensions ◽  
One Dimension ◽  
Simons Theory ◽  
Two Dimensional ◽  
Dual Theory ◽  
Recent Developments ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1)2D Chern-Simons theory than like Einstein gravity.

scholarly journals Symmetry-resolved entanglement in AdS3/CFT2 coupled to U(1) Chern-Simons theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Suting Zhao ◽  
Christian Northe ◽  
René Meyer
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Field ◽  
Wilson Line ◽  
Entanglement Entropy ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We consider symmetry-resolved entanglement entropy in AdS3/CFT2 coupled to U(1) Chern-Simons theory. We identify the holographic dual of the charged moments in the two-dimensional conformal field theory as a charged Wilson line in the bulk of AdS3, namely the Ryu-Takayanagi geodesic minimally coupled to the U(1) Chern-Simons gauge field. We identify the holonomy around the Wilson line as the Aharonov-Bohm phases which, in the two-dimensional field theory, are generated by charged U(1) vertex operators inserted at the endpoints of the entangling interval. Furthermore, we devise a new method to calculate the symmetry resolved entanglement entropy by relating the generating function for the charged moments to the amount of charge in the entangling subregion. We calculate the subregion charge from the U(1) Chern-Simons gauge field sourced by the bulk Wilson line. We use our method to derive the symmetry-resolved entanglement entropy for Poincaré patch and global AdS3, as well as for the conical defect geometries. In all three cases, the symmetry resolved entanglement entropy is determined by the length of the Ryu-Takayanagi geodesic and the Chern-Simons level k, and fulfills equipartition of entanglement. The asymptotic symmetry algebra of the bulk theory is of $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody type. Employing the $$ \hat{\mathfrak{u}}{(1)}_k $$ u ̂ 1 k Kac-Moody symmetry, we confirm our holographic results by a calculation in the dual conformal field theory.

scholarly journals STATIC POTENTIAL AND A NEW GENERALIZED CONNECTION IN THREE DIMENSIONS

2004 ◽  
Vol 19 (22) ◽  
pp. 1695-1700 ◽  
Author(s):  
PATRICIO GAETE
Keyword(s):  
Gauge Theory ◽  
Three Dimensions ◽  
Simons Theory ◽  
Static Potential ◽  
Gauge Invariant ◽  
Confining Potential ◽  
Static Interaction ◽  
Pure Gauge Theory ◽  
Chern Simons ◽  
Chern Simons Theory

For a recently proposed pure gauge theory in three dimensions, without a Chern–Simons term, we calculate the static interaction potential within the structure of the gauge-invariant variables formalism. As a consequence, a confining potential is obtained. This result displays a marked qualitative departure from the usual Maxwell–Chern–Simons theory.

Superconducting phase transition in a two-dimensional Chern-Simons theory

1991 ◽  
Vol 44 (14) ◽  
pp. 7519-7525 ◽  
Author(s):  
J. Kapusta ◽  
M. E. Carrington ◽  
B. Bayman ◽  
D. Seibert ◽  
C. S. Song
Keyword(s):  
Phase Transition ◽  
Superconducting Phase ◽  
Simons Theory ◽  
Two Dimensional ◽  
Chern Simons ◽  
Superconducting Phase Transition ◽  
Chern Simons Theory

COHERENT STATE QUANTIZATION OF CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (05) ◽  
pp. 959-988 ◽  
Author(s):  
MICHIEL BOS ◽  
V.P. NAIR
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Coherent State ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Simons Theory ◽  
Two Dimensional ◽  
Conformal Field ◽  
Chern Simons ◽  
Chern Simons Theory

Three-dimensional Chern-Simons gauge theories are quantized in a functional coherent state formalism. The connection with two-dimensional conformal field theory is found to emerge naturally. The normalized wave functionals are identified as generating functionals for the chiral blocks of two-dimensional current algebra.

scholarly journals Topological strings, two-dimensional Yang-Mills theory and Chern-Simons theory on torus bundles

2008 ◽  
Vol 12 (5) ◽  
pp. 981-1058 ◽  
Author(s):  
Nicola Caporaso ◽  
Michele Cirafici ◽  
Luca Griguolo ◽  
Sara Pasquetti ◽  
Domenico Seminara ◽  
...  
Keyword(s):  
Topological Strings ◽  
Simons Theory ◽  
Two Dimensional ◽  
Yang Mills ◽  
Torus Bundles ◽  
Chern Simons ◽  
Chern Simons Theory

D = 3 Gauge Dynamics: Yang-Mills and Yang-Mills-Chern-Simons Theory

1997 ◽  
Vol 12 (06) ◽  
pp. 1023-1031 ◽  
Author(s):  
John M. Cornwall
Keyword(s):  
Three Dimensions ◽  
Simons Theory ◽  
Dynamical Mass ◽  
Yang Mills ◽  
Quantum Vortex ◽  
Dynamical Generation ◽  
Perturbative Regime ◽  
Vortex Solitons ◽  
Chern Simons ◽  
Chern Simons Theory

We summarize recent progress in understanding non-perturbative effects of Yang-Mills (YM) and Yang-Mills Chern-Simons (YMCS) theories in three dimensions, based on a monopole-vortex vacuum condensate. In YM theory these include dynamical generation of a gluon mass, quantum vortex solitons, and and entropy-driven condensate of these solitons. This leads to confinement as well as CS fluctuations (related to B+L violation). These two phenomena are both described in terms of topological linkings of closed vortices with a Wilson loop (confinement) or with each other (CS fluctuations). In SU(N) YMCS theory with a level-k CS term, similar effects occur for k less than a critical value kc ≈ 2N, while for larger k there is a phase transition to a purely perturbative regime with no dynamical mass (just the perturbative CS mass), solitons, or condensate.

REMARKS ON FERMION–BOSON EQUIVALENCE IN THREE DIMENSIONS

1999 ◽  
Vol 14 (04) ◽  
pp. 307-315 ◽  
Author(s):  
A. DE SOUZA DUTRA ◽  
C. P. NATIVIDADE
Keyword(s):  
Quantum Theory ◽  
Thirring Model ◽  
The Self ◽  
Three Dimensions ◽  
Simons Theory ◽  
Dual Model ◽  
Third Order ◽  
Chern Simons ◽  
Chern Simons Theory

Starting from a decomposition of the self-dual field in (2+1) dimensions, we build up an alternative quantum theory which consists of a self-dual model coupled to a Maxwell-generalized Chern–Simons theory. We discuss the fermion–boson equivalence of this quantum theory by comparing it with the Thirring model. Using these results we were able to compute the mass of the bosonized fermions up to third order in 1/m. Some problems related to the number of poles of the effective propagator are also addressed.

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