Schwarzian quantum mechanics as a Drinfeld-Sokolov reduction of 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.

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Chern–Simons gauge theory and symplectic quantum mechanics

Canadian Journal of Physics ◽

10.1139/cjp-2014-0563 ◽

2015 ◽

Vol 93 (9) ◽

pp. 971-973

Author(s):

Lisa Jeffrey

Keyword(s):

Quantum Mechanics ◽

Gauge Theory ◽

Partition Function ◽

Partition Functions ◽

Action Functional ◽

Symplectic Action ◽

Chern Simons

We describe the relation between the Chern–Simons gauge theory partition function and the partition function defined using the symplectic action functional as the Lagrangian. We show that the partition functions obtained using these two Lagrangians agree, and we identify the semiclassical formula for the partition function defined using the symplectic action functional. We also compute the semiclassical formulas for the partition functions obtained using the two different Lagrangians: the Chern–Simons functional and the symplectic action functional.

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TWO-DIMENSIONAL LATTICE GRAVITY AS A SPIN SYSTEM

International Journal of Modern Physics C ◽

10.1142/s0129183194000490 ◽

1994 ◽

Vol 05 (02) ◽

pp. 359-361 ◽

Cited By ~ 11

Author(s):

W. BEIRL ◽

H. MARKUM ◽

J. RIEDLER

Keyword(s):

Partition Function ◽

External Field ◽

Path Integral ◽

Spin System ◽

Higher Dimensions ◽

Two Dimensional ◽

Path Integral Formulation ◽

Regge Calculus ◽

Dimensional Lattice ◽

Matter Fields

Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin system with higher couplings on a Kagomé lattice. Various measures acting as external field are considered. Extensions to matter fields and higher dimensions are discussed.

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The two-sphere partition function in two-dimensional quantum gravity

Journal of High Energy Physics ◽

10.1007/jhep09(2021)116 ◽

2021 ◽

Vol 2021 (9) ◽

Cited By ~ 1

Author(s):

Dionysios Anninos ◽

Teresa Bautista ◽

Beatrix Mühlmann

Keyword(s):

Partition Function ◽

Quantum Gravity ◽

Cosmological Constant ◽

Path Integral ◽

Central Charge ◽

Liouville Theory ◽

Two Dimensional ◽

Positive Cosmological Constant ◽

Gauge Fixing ◽

Semiclassical Expansion

Abstract We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.

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The two-sphere partition function in two-dimensional quantum gravity at fixed area

Journal of High Energy Physics ◽

10.1007/jhep09(2021)189 ◽

2021 ◽

Vol 2021 (9) ◽

Author(s):

Beatrix Mühlmann

Keyword(s):

Partition Function ◽

Quantum Gravity ◽

Path Integral ◽

Central Charge ◽

Gravity Theory ◽

Feynman Diagrams ◽

Two Dimensional ◽

Loop Order ◽

Fixed Area

Abstract We discuss two-dimensional quantum gravity coupled to conformal matter and fixed area in a semiclassical large and negative matter central charge limit. In this setup the gravity theory — otherwise highly fluctuating — admits a round two-sphere saddle. We discuss the two-sphere partition function up to two-loop order from the path integral perspective. This amounts to studying Feynman diagrams incorporating the fixed area constraint on the round two-sphere. In particular we find that all ultraviolet divergences cancel to this order. We compare our results with the two-sphere partition function obtained from the DOZZ formula.

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The disk partition function in string theory

Journal of High Energy Physics ◽

10.1007/jhep08(2021)026 ◽

2021 ◽

Vol 2021 (8) ◽

Author(s):

Lorenz Eberhardt ◽

Sridip Pal

Keyword(s):

String Theory ◽

Partition Function ◽

Gauge Group ◽

Path Integral ◽

Open String ◽

Infinite Volume ◽

Conformal Gauge ◽

Negative Volume

Abstract We investigate the disk partition function for the open string. This is a subtle problem because of the presence of a residual gauge group PSL(2, ℝ) on the worldsheet even after fixing the conformal gauge. It naively has infinite volume and leads to a vanishing answer. We use different methods that all demonstrate that PSL(2, ℝ) effectively behaves like a group with finite negative volume in the path integral, which leads to a simple prescription for the computation of the disk partition function. We apply our findings to give a simple rederivation of the D-brane tensions.

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SUSCEPTIBILITY FOR 2-d GRAVITY COUPLED TO SO(2,1) BF SYSTEM

Modern Physics Letters A ◽

10.1142/s0217732391003468 ◽

1991 ◽

Vol 06 (32) ◽

pp. 2965-2972

Author(s):

MARCO PICCO ◽

JEAN-CHRISTOPHE WALLET

Keyword(s):

Partition Function ◽

Gauge Group ◽

Two Dimensional ◽

Continuum Approach ◽

Topological Theory ◽

Dimensional Gravity ◽

The Continuum

We consider two-dimensional gravity in the presence of a system of fields described by an action which can be derived from a topological theory with gauge group SO(2,1). Working in the continuum approach, we extract the area dependence of the partition function and deduce the susceptibility for the theory. The inclusion of D massless scalars gives a susceptibility depending linearly on D. We finally discuss our results.

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QUANTUM YANG-MILLS THEORY ON ARBITRARY SURFACES

International Journal of Modern Physics A ◽

10.1142/s0217751x9200168x ◽

1992 ◽

Vol 07 (16) ◽

pp. 3781-3806 ◽

Cited By ~ 65

Author(s):

MATTHIAS BLAU ◽

GEORGE THOMPSON

Keyword(s):

Partition Function ◽

Path Integral ◽

Two Dimensional ◽

Expectation Values ◽

Gauge Transformations ◽

Yang Mills ◽

Integral Methods ◽

Closed Surfaces ◽

Abelian Case

We study quantum Maxwell and Yang-Mills theory on orientable two-dimensional surfaces with an arbitrary number of handles and boundaries. Using path integral methods we derive general and explicit expressions for the partition function and expectation values of contractible and noncontractible Wilson loops on closed surfaces of any genus, as well as for the kernels on manifolds with handles and boundaries. In the Abelian case we also compute correlation functions of intersecting and self-intersecting loops on closed surfaces, and discuss the role of large gauge transformations and topologically nontrivial bundles.

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TWO-DIMENSIONAL QUANTUM GRAVITY WITH GENERALIZED ACTION AND COMPACT BOSON

Modern Physics Letters A ◽

10.1142/s0217732391002104 ◽

1991 ◽

Vol 06 (21) ◽

pp. 1953-1959 ◽

Cited By ~ 27

Author(s):

I. M. LICHTZIER ◽

S. D. ODINTSOV

Keyword(s):

Partition Function ◽

Quantum Gravity ◽

Path Integral ◽

Two Dimensional

The generalized 2-dimensional quantum gravity is considered. The path-integral is evaluated without the need to impose the restrictions on the dimensions of matter. The partition function as well as Hagedorn temperature is also calculated for the case when one boson is compact.

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