Topological Conformal Field Theory from the Point of View of Integrable Systems

1993 ◽  
pp. 283-302 ◽  
Author(s):  
B. Dubrovin
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Integrable Systems ◽  
Point Of View ◽  
Conformal Field ◽  
Topological Conformal Field Theory

Krichever-Novikov formulation of topological conformal field theory

1991 ◽  
Vol 23 (4) ◽  
pp. 271-277 ◽  
Author(s):  
Alok Kumar ◽  
Jnanadeva Maharana ◽  
Gautam Sengupta
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Field ◽  
Topological Conformal Field Theory

scholarly journals CONFORMAL MAPPING OF UNRUH TEMPERATURE

2009 ◽  
Vol 24 (19) ◽  
pp. 1473-1483 ◽  
Author(s):  
PIERRE MARTINETTI
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Conformal Mapping ◽  
Thermal State ◽  
Minkowski Spacetime ◽  
Conformal Factor ◽  
Point Of View ◽  
Double Cone ◽  
Mathematical Point ◽  
Conformal Field

In the framework of conformal field theory, the mapping from (unbounded) wedge regions of Minkowski spacetime to (bounded) double-cone regions is extended to the Unruh temperature associated to a uniformly accelerated observer. The link between a previous result, the diamond's temperature, and the conformal factor (Weyl rescaling of the metric) is worked out. One thus explains from a mathematical point of view why an observer with finite lifetime experiences the vacuum as a thermal state whatever his acceleration, even vanishing.

scholarly journals INTRODUCTION TO VERTEX ALGEBRAS, BORCHERDS ALGEBRAS AND THE MONSTER LIE ALGEBRA

1993 ◽  
Vol 08 (31) ◽  
pp. 5441-5503 ◽  
Author(s):  
REINHOLD W. GEBERT
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Lie Algebra ◽  
Point Of View ◽  
Vertex Algebras ◽  
Affine Lie Algebras ◽  
Conformal Field ◽  
Formal Calculus ◽  
Developing Area ◽  
Definition Of

The theory of vertex algebras constitutes a mathematically rigorous axiomatic formulation of the algebraic origins of conformal field theory In this context Borcherds algebras arise as certain “physical” subspaces of vertex algebras. The aim of this review is to give a pedagogical introduction to this rapidly developing area of mathematics. Based on the machinery of formal calculus, we present the axiomatic definition of vertex algebras. We discuss the connection with conformal field theory by deriving important implications of these axioms. In particular, many explicit calculations are presented to stress the eminent role of the Jacobi identity axiom for vertex algebras. As a class of concrete examples the vertex algebras associated with even lattices are constructed and it is shown in detail how affine Lie algebras and the fake monster Lie algebra naturally appear. This leads us to the abstract definition of Borcherds algebras as generalized Kac-Moody algebras and their basic properties. Finally, the results about the simplest generic Borcherds algebras are analyzed from the point of view of symmetry in quantum theory and the construction of the monster Lie algebra is sketched.

scholarly journals AN ALGEBRAIC APPROACH TO LOGARITHMIC CONFORMAL FIELD THEORY

2003 ◽  
Vol 18 (25) ◽  
pp. 4593-4638 ◽  
Author(s):  
MATTHIAS R. GABERDIEL
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Algebraic Approach ◽  
Point Of View ◽  
Algebraic Point ◽  
Conformal Field ◽  
Logarithmic Conformal Field Theory ◽  
Comprehensive Introduction

A comprehensive introduction to logarithmic conformal field theory, using an algebraic point of view, is given. A number of examples are explained in detail, including the c=-2 triplet theory and the k=-4/3 affine su(2) theory. We also give some brief introduction to the work of Zhu.

scholarly journals PERTURBATIVE DEFORMATIONS OF CONFORMAL FIELD THEORIES REVISITED

2010 ◽  
Vol 22 (02) ◽  
pp. 117-192
Author(s):  
IGOR KRIZ
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Mirror Symmetry ◽  
Free Field ◽  
K3 Surfaces ◽  
Point Of View ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Conformal Field ◽  
Gepner Model

The purpose of this paper is to revisit the theory of perturbative deformations of conformal field theory from a mathematically rigorous, purely worldsheet point of view. We specifically include the case of N = (2,2) conformal field theories. From this point of view, we find certain surprising obstructions, which appear to indicate that contrary to previous findings, not all deformations along marginal fields exist perturbatively. This includes the case of deformation of the Gepner model of the Fermat quintic along certain cc fields. In other cases, including Gepner models of K3-surfaces and the free field theory, our results coincides with known predictions. We give partial interpretation of our results via renormalization and mirror symmetry.

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