scholarly journals TRACE ANOMALIES AND COCYCLES OF WEYL AND DIFFEOMORPHISMS GROUPS

1996 ◽  
Vol 11 (05) ◽  
pp. 409-421 ◽  
Author(s):  
D.R. KARAKHANYAN ◽  
R.P. MANVELYAN ◽  
R.L. MKRTCHYAN
Keyword(s):  
Partition Function ◽  
Weyl Group ◽  
Simple Form ◽  
General Structure ◽  
Consistency Condition ◽  
General Rule ◽  
Two Dimensional ◽  
Conformal Invariant ◽  
Trace Anomaly ◽  
Liouville Action

The general structure of trace anomaly, suggested recently by Deser and Schwimmer is argued to be the consequence of the Wess-Zumino consistency condition. The response of partition function on a finite Weyl transformation, which is connected with the cocycles of the Weyl group in d=2k dimensions is considered, and explicit answers for d=4, 6 are obtained. In particular, it is shown that addition of the special combination of the local counterterms leads to the simple form of that cocycle, quadratic over Weyl field σ, i.e. the form, similar to the two-dimensional Liouville action. This form also establishes the connection of the cocycles with conformal-invariant operators of order d and zero weight. We also give the general rule for transformation of that cocycles into the cocycles of diffeomorphisms group.

scholarly journals BMS field theories and Weyl anomaly

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Arjun Bagchi ◽  
Sudipta Dutta ◽  
Kedar S. Kolekar ◽  
Punit Sharma
Keyword(s):  
Three Dimensions ◽  
Field Theories ◽  
Partition Functions ◽  
Two Dimensional ◽  
Speed Of Light ◽  
Asymptotically Flat ◽  
Weyl Invariance ◽  
Flat Spacetimes ◽  
Liouville Action ◽  
Null Surfaces

Abstract Two dimensional field theories with Bondi-Metzner-Sachs symmetry have been proposed as duals to asymptotically flat spacetimes in three dimensions. These field theories are naturally defined on null surfaces and hence are conformal cousins of Carrollian theories, where the speed of light goes to zero. In this paper, we initiate an investigation of anomalies in these field theories. Specifically, we focus on the BMS equivalent of Weyl invariance and its breakdown in these field theories and derive an expression for Weyl anomaly. Considering the transformation of partition functions under this symmetry, we derive a Carrollian Liouville action different from ones obtained in the literature earlier.

scholarly journals Multiple phases in a generalized Gross-Witten-Wadia matrix model

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jorge G. Russo ◽  
Miguel Tierz
Keyword(s):  
Partition Function ◽  
Matrix Models ◽  
Characteristic Polynomial ◽  
Matrix Model ◽  
Phase Structure ◽  
Unitary Matrix ◽  
Two Dimensional ◽  
Toeplitz Determinants ◽  
Dimensional Parameter ◽  
Planar Limit

Abstract We study a unitary matrix model of the Gross-Witten-Wadia type, extended with the addition of characteristic polynomial insertions. The model interpolates between solvable unitary matrix models and is the unitary counterpart of a deformed Cauchy ensemble. Exact formulas for the partition function and Wilson loops are given in terms of Toeplitz determinants and minors and large N results are obtained by using Szegö theorem with a Fisher-Hartwig singularity. In the large N (planar) limit with two scaled couplings, the theory exhibits a surprisingly intricate phase structure in the two-dimensional parameter space.

scholarly journals Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of BF theory

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Fridrich Valach ◽  
Donald R. Youmans
Keyword(s):  
Quantum Mechanics ◽  
Partition Function ◽  
Gauge Group ◽  
Path Integral ◽  
Coadjoint Orbits ◽  
Two Dimensional ◽  
Edge States ◽  
Class Constraint ◽  
Action Functional ◽  
Bf Theory

Abstract We give an interpretation of the holographic correspondence between two-dimensional BF theory on the punctured disk with gauge group PSL(2, ℝ) and Schwarzian quantum mechanics in terms of a Drinfeld-Sokolov reduction. The latter, in turn, is equivalent to the presence of certain edge states imposing a first class constraint on the model. The constrained path integral localizes over exceptional Virasoro coadjoint orbits. The reduced theory is governed by the Schwarzian action functional generating a Hamiltonian S1-action on the orbits. The partition function is given by a sum over topological sectors (corresponding to the exceptional orbits), each of which is computed by a formal Duistermaat-Heckman integral.

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

SYMMETRY IN TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (13) ◽  
pp. 2331-2346 ◽  
Author(s):  
KAI-WEN XU ◽  
CHUAN-JIE ZHU
Keyword(s):  
Light Cone ◽  
Integration Method ◽  
Symmetry Algebra ◽  
Two Dimensional ◽  
Light Cone Gauge ◽  
Simple Interpretation ◽  
Brst Charge ◽  
Dimensional Gravity ◽  
Covariant Gauge ◽  
Liouville Action

We study the symmetry of two-dimensional gravity by choosing a generic gauge. A local action is derived which reduces to either the Liouville action or the Polyakov one by reducing to the conformal or light-cone gauge respectively. The theory is also solved classically. We show that an SL (2, R) covariant gauge can be chosen so that the two-dimensional gravity has a manifest Virasoro and the sl (2, R)-current symmetry discovered by Polyakov. The symmetry algebra of the light-cone gauge is shown to be isomorphic to the Beltrami algebra. By using the contour integration method we construct the BRST charge QB corresponding to this algebra following the Fradkin-Vilkovisky procedure and prove that the nilpotence of QB requires c=28 and α0=1. We give a simple interpretation of these conditions.

The partition function of two-dimensional quantum gravity

1989 ◽  
Vol 233 (1-2) ◽  
pp. 79-84 ◽  
Author(s):  
M.A. Awada ◽  
A.H. Chamseddine
Keyword(s):  
Partition Function ◽  
Quantum Gravity ◽  
Two Dimensional
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