Sebastian Jaimungal

Universality in effective strings

It is demonstrated that, due to the finite thickness of domain walls and the consequent ambiguity in defining their locations, the effective string description obtained by integrating out bulk degrees of freedom contains ambiguities in the coefficients of the various geometric terms. The only term with unambiguous coefficient is the zeroth-order Nambu-Goto term. We argue that fermionic ghost fields which implement gauge-fixing act to balance these ambiguities. The renormalized string tension, obtained after integrating out both bulk and world sheet degrees of freedom, can be defined in a scheme-independent manner; explicit finite expressions are computed, to one-loop, for the case of compact quantum electrodynamics and ϕ4 theory.

WILSON LOOPS, BIANCHI CONSTRAINTS AND DUALITY IN ABELIAN LATTICE MODELS

Abstract We introduce new modified abelian lattice models, with inhomogeneous local interactions, in which a sum over topological sectors are included in the defining partition function. The dual models, on lattices with arbitrary topology, are constructed and they are found to contain sums over topological sectors, with modified groups, as in the original model. The role of the sum over sectors is illuminated by deriving the field-strength formulation of the models in an explicitly gauge-invariant manner. The field strengths are found to satisfy, in addition to the usual local Bianchi constraints, global constraints. We demonstrate that the sum over sectors removes these global constraints and consequently softens the quantization condition on the global charges in the system. Duality is also used to construct mappings between the order and disorder variables in the theory and is dual. A consequence of the duality transformation is that correlators which wrap around non-trivial cycles of the lattice vanish identically. For particular dimensions this mapping allows an explicit expression for arbitrary correlators to be obtained.

LOOPS, SURFACES AND GRASSMANN REPRESENTATION IN TWO- AND THREE-DIMENSIONAL ISING MODELS

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

Topology and duality in abelian lattice theories

Abstract We show how to obtain the dual of any lattice model, with inhomogeneous local interactions, based on an arbitrary Abelian group in any dimension and on lattices with arbitrary topology. It is shown that in general the dual theory contains disorder loops on the generators of the cohomology group of a particular dimension. An explicit construction for altering the statistical sum to obtain a self-dual theory, when these obstructions exist, is also given. We discuss some applications of these results, particularly the existence of non-trivial self-dual 2-dimensional Z N theories on the torus. In addition, we explicitly construct the n-point functions of plaquette variables for the U(1) gauge theory on the 2-dimensional g-tori.

THETA SECTORS AND THERMODYNAMICS OF A CLASSICAL ADJOINT GAS

Abstract The effect of topology on the thermodynamics of a gas of adjoint representation charges interacting via 1 + 1-dimensional SU ( N ) gauge fields is investigated. We demonstrate explicitly the existence of multiple vacua parameterized by the discrete superselection variable k = I , … , N . In the low pressure limit, the k dependence of the adjoint gas equation of state is calculated and shown to be non-trivial. Conversely, in the limit of high system pressure, screening by the adjoint charges results in an equation of state independent of k. Additionally, the relation of this model to adjoint QCD at finite temperature in two dimensions and the limit N → ∞ are discussed.

Phase transition in quantum gravity

A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some approximation. We outline a quantum field theory calculation, based on general relativity as the classical theory, which implies a phase transition in quantum gravity. The order parameters are composite fields derived from spacetime metric functions. These are massless below a critical energy scale and become massive above it. There is a corresponding breaking of classical symmetry.

PHASE TRANSITION IN QUANTUM GRAVITY

A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that nonperturbative effects can be computed, at least in some approximation. We outline a quantum field theory calculation, based on general relativity as the classical theory, which implies a phase transition in quantum gravity. The order parameters are composite fields derived from space–time metric functions. These are massless below a critical energy scale and become massive above it. There is a corresponding breaking of classical symmetry.

T-duality in lattice regularized σ-models

Abstract It is shown that when the underlying sigma model of bosonic string theory is written in terms of single-valued fields, which live in the covering space of the target space, Abelian T -duality survives lattice regularization of the world-sheet. The projection onto the target-space is implemented through a sum over cohomology, which bears resemblance to summing over topological sectors in Yang-Mills theories. In particular, the case of string theory on a circle is shown to be explicitly self-dual in the lattice regulated model and automatically forbids vortex excitations which would otherwise destroy the duality. For other target spaces a generalized notion of T -duality is observed in which the target space and the cohomology coefficient group are interchanged under duality. Specific examples show that the fundamental group of the target space may not be preserved in the T -dual theory. Generalized models which exhibit T -duality behaviour, with dynamical variables that live on the k -dimensional cells of ( p +1)-dimensional world-volumes, are also constructed. These models correspond to gauge theories, and higher-dimensional analogues, in which one sums over various topological sectors of the theory.