Amitabha Lahiri

Parallel Transport over Path Spaces

We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework.

Renormalizability of the dynamical two-form

A proof of renormalizability of the theory of the dynamical non-Abelian two-form is given using the Zinn-Justin equation. Two previously unknown symmetries of the quantum action, different from the BRST symmetry, are needed for the proof. One of these is a gauge fermion dependent nilpotent symmetry, while the other mixes different fields with the same transformation properties. The BRST symmetry itself is extended to include a shift transformation by use of an anticommuting constant. These three symmetries restrict the form of the quantum action up to arbitrary order in perturbation theory. The results show that it is possible to have a renormalizable theory of massive vector bosons in four dimensions without a residual Higgs boson.

Mass function and particle creation in Schwarzschild–de Sitter spacetime

We construct a mass or energy function for the non-Nariai class Schwarzschild–de Sitter black hole spacetime in the region between the black hole and the cosmological event horizons. The mass function is local, positive definite, continuous and increases monotonically with the radial distance from the black hole event horizon. We derive the Smarr formula using this mass function, and demonstrate that the mass function reproduces the two-temperature Schwarzschild–de Sitter black hole thermodynamics, along with a term corresponding to the negative pressure due to positive cosmological constant. We further give a field theoretic derivation of the particle creation by both the horizons and discuss its connection with the mass function.

Topologically massive non-Abelian gauge theories: Constraints and deformations

We study the relationship between three non-Abelian topologically massive gauge theories, viz., the naive non-Abelian generalization of the Abelian model, Freedman-Townsend model, and the dynamical 2-form theory, in the canonical framework. The Hamiltonian formulation of the naive non-Abelian theory is presented first. The other two non-Abelian models are obtained by deforming the constraints of this model. We study the role of the auxiliary vector field in the dynamical 2-form theory in the canonical framework and show that the dynamical 2-form theory cannot be considered as the embedded version of the naive non-Abelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.

Masses of Physical Scalars in Two Higgs Doublet Models

We study the implication of a criterion of naturalness for two Higgs doublet models (2HDMs) with an additional U(1) symmetry. In particular, we assume the cancellation of quadratic divergences in 2HDMs resulting in the Veltman conditions. Assuming that the lighter uncharged scalar is the observed Higgs particle of mass 125 GeV [1, 2], and imposing further the constraints from the electroweak T-parameter , stability, and perturbative unitarity produces a range for the masses of each of the remaining physical scalars.

Effect of a positive cosmological constant on cosmic strings

We study cosmic Nielsen-Olesen strings in space-times with a positive cosmological constant. For the free cosmic string in a cylindrically symmetric space-time, we calculate the contribution of the cosmological constant to the angle deficit, and to the bending of null geodesics. For a cosmic string in a Schwarzschild-de Sitter space-time, we use Kruskal patches around the inner and outer horizons to show that a thin string can pierce them.

Kaluza Ansatz applied to Eddington inspired Born-Infeld Gravity

We apply Kaluza’s procedure to Eddington-inspired Born-Infeld action in gravity in five dimensions. The resulting action contains, in addition to the usual four-dimensional actions for gravity and electromagnetism, nonlinear couplings between the electromagnetic field strength and curvature. Considering the spherically symmetric solution as an example we find the lowest order � ,

No hair theorems for stationary axisymmetric black holes

AbstractWe present a non-perturbative proof of the no hair theorems corresponding to scalar and Procafields for stationary axisymmetric de Sitter black hole spacetimes. Our method also applies toasymptotically flat and under a reasonable assumption, to asymptotically anti-de Sitter spacetimes.Keywords: Stationary black holes, no hair theorem, de Sitter 1 Introduction The classical no hair conjecture for black holes states that any gravitational collapse reaches a finalstationary state characterized only by a small number of parameters. A part of this conjecturehas been proven rigorously by taking different matter fields, known as the no hair theorem (seee.g. [1, 2, 3]) and deals with the uniqueness of stationary black hole solutions characterized onlyby mass, angular momentum, and charges corresponding to long range gauge fields such as theelectromagnetic field. Any non-trivial field configuration other than the long range gauge fieldspresent at the exterior of a stationary black hole is known as ‘hair’. In particular, it has beenshown that static, spherically symmetric black holes do not support hair corresponding to scalarsin convex potentials, Proca-massive vector fields [4], or even gauge fields corresponding to theAbelian Higgs model [5, 6].All the above proofs assume the spacetime to be asymptotically flat, i.e., one can reach spacelikeinfinity so that sufficiently rapid fall-off conditions on the matter fields can be imposed there. Butrecent observations [7, 8] suggest that there is a strong possibility that our universe is endowedwith a small but positive cosmological constant Λ. It is generally expected that in that case thespacetime in its stationary state should have an outer or cosmological Killing horizon [9]. Thecosmological Killing horizon acts in general as a causal boundary (see e.g. [10]) so that no physicalobserver can communicate beyond this horizon along a future directed path. If there is a black

NEGATIVE FORMS AND PATH SPACE FORMS

We present an account of negative differential forms within a natural algebraic framework of differential graded algebras, and explain their relationship with forms on path spaces.

Generalized forms and vector fields

The generalized vector is defined on an n-dimensional manifold. The interior product and Lie derivative acting on generalized p-forms, −1 ≤ p ≤ n are introduced. The generalized commutator of two generalized vectors is defined. Adding a correction term to Cartans formula, the generalized Lie derivatives action on a generalized vector field is defined. We explore various identities of the generalized Lie derivative with respect to generalized vector fields, and discuss an application.