Central charge, trace and gravitational anomalies in two dimensions

1988 ◽  
Vol 38 (8) ◽  
pp. 2482-2489 ◽  
Author(s):  
E. Guadagnini
Keyword(s):  
Central Charge ◽  
Two Dimensions ◽  
Gravitational Anomalies

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

scholarly journals Boundary states for chiral symmetries in two dimensions

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Philip Boyle Smith ◽  
David Tong
Keyword(s):  
Boundary Conditions ◽  
Ground State ◽  
Zero Mode ◽  
Central Charge ◽  
Two Dimensions ◽  
Dirac Fermions ◽  
Chiral Symmetries ◽  
Boundary States ◽  
Ground State Degeneracy ◽  
Left And Right

Abstract We study boundary states for Dirac fermions in d = 1 + 1 dimensions that preserve Abelian chiral symmetries, meaning that the left- and right-moving fermions carry different charges. We derive simple expressions, in terms of the fermion charge assignments, for the boundary central charge and for the ground state degeneracy of the system when two different boundary conditions are imposed at either end of an interval. We show that all such boundary states fall into one of two classes, related to SPT phases supported by (−1)F , which are characterised by the existence of an unpaired Majorana zero mode.

Gauge and gravitational anomalies in two dimensions

1987 ◽  
Vol 35 (4) ◽  
pp. 1268-1279 ◽  
Author(s):  
Dae Sung Hwang
Keyword(s):  
Two Dimensions ◽  
Gravitational Anomalies

REMARKS ON THE MODEL WITH LOCAL U(1)V×U(1)A SYMMETRY IN TWO DIMENSIONS

1991 ◽  
Vol 06 (14) ◽  
pp. 1291-1298 ◽  
Author(s):  
YOSHIYUKI WATABIKI
Keyword(s):  
Energy Momentum Tensor ◽  
Central Charge ◽  
Axial Vector ◽  
Local Symmetry ◽  
Momentum Tensor ◽  
Two Dimensions ◽  
Global Symmetry ◽  
Supersymmetric Extension ◽  
Commutator Algebra ◽  
Local Vector

We investigate a 2-dimensional model which possesses a local vector U (1)V and axial vector U (1)A symmetry. We obtain a general form of Lagrangian which possesses this local symmetry. We also investigate the global symmetry aspects of the model. The commutator algebra of the energy-momentum tensor and the currents is derived, and the central charge of the model is calculated. Supersymmetric extension of the model is also studied.

scholarly journals DUAL GENERALIZATIONS OF SINE–GORDON FIELD THEORY AND INTEGRABILITY SUBMANIFOLDS IN PARAMETER SPACE

2000 ◽  
Vol 15 (21) ◽  
pp. 3315-3340
Author(s):  
P. BASEILHAC ◽  
D. REYNAUD
Keyword(s):  
Field Theory ◽  
Parameter Space ◽  
Complex Space ◽  
Central Charge ◽  
Two Dimensions ◽  
Field Theories ◽  
Complex Numbers ◽  
Quantum Field Theories ◽  
Conformal Field ◽  
Extended Complex

The dual relationship between two n-1 parameter families of quantum field theories based on extended complex numbers is investigated in two dimensions. The nonlocal conserved charges approach is used. The lowest rank affine Toda field theories are generated and identified as integrability submanifolds in parameter space. A truncation of the model leads to a conformal field theory in extended complex space. Depending on the projection over the usual complex space chosen, a parametrized central charge is calculated.

scholarly journals SUPER WEYL ANOMALIES IN THE AdS/CFT CORRESPONDENCE

1999 ◽  
Vol 14 (23) ◽  
pp. 3731-3743 ◽  
Author(s):  
MADOKA NISHIMURA ◽  
YOSHIAKI TANII
Keyword(s):  
Central Charge ◽  
Two Dimensions ◽  
Field Theories ◽  
Conformal Supergravity ◽  
Superconformal Field Theories ◽  
Axial Gauge ◽  
Vector Gauge

Anomalies of N=(4,4) superconformal field theories coupled to a conformal supergravity background in two dimensions are computed by using the AdS/CFT correspondence. We find that Weyl, axial gauge and super Weyl transformations are anomalous, while general coordinate, local Lorentz, vector gauge and local supertransformations are not. The coefficients of the anomalies show that the superconformal field theories have the central charge expected in the AdS/CFT correspondence.

DIMERS AND SPANNING TREES: SOME RECENT RESULTS

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1951-1961 ◽  
Author(s):  
F. Y. WU
Keyword(s):  
Spanning Tree ◽  
Recent Progress ◽  
Spanning Trees ◽  
Central Charge ◽  
Laplacian Matrix ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Eigenvalues Of The Laplacian ◽  
Text Correction ◽  
Orientable Surfaces

This paper reviews some recent progress on dimer and spanning tree enumerations. We use the Kasteleyn formulation to enumerate close-packed dimers on a simple-quartic net embedded on non-orientable surfaces, and obtain solutions in the form of double products. For spanning trees the enumeration is carried out by evaluating the eigenvalues of the Laplacian matrix associated with the lattice, a procedure which holds in any spatial dimension. In two dimensions a bijection due to Temperley relates spanning tree and dimer configurations on two related lattices. We use this bijection to enumerate dimers on a net with a vacancy on the boundary. It is found that the occurrence of a vacancy induces a [Formula: see text] correction to the enumeration, where N is the linear size of the lattice, and changes the central charge from c = 1 to -2.

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