Samir K. Paul

Charged vortices in an abelian Higgs model with Chern-Simons term

Abstract The existence is shown of charged vortices of finite energy in a (2+1)-dimensional abelian Higgs model with Chern-Simons (C-S) term. Further, lower bounds on the energy and angular momentum of these vortices are obtained. Finally it is shown that the “glueballs” are absent in (2+1)-dimensional QED or QCD with C-S term for any compact gauge group.

Self-dual factorization of the Proca equation with Chern-Simons term in 4K − 1 dimensions

We show that the Proca equation with Chern-Simons term propagates a self-dual field with two distinct masses in 4K − 1 dimensions. In the special case of three-dimensions (K = 1) it is further shown that the corresponding lagrangian is the free gauge part of the abelian Higgs model with Chern-Simons term after the Higgs mechanism has taken place. Some unusual features of the nonabelian Higgs model with Chern-Simons term are also pointed out.

THE INTERACTION OF CHERN-SIMONS VORTICES

We study the interaction between two vortices in the Abelian Higgs model with an added term of the Chern-Simons form. We argue that our results may be relevant to the physics of high temperature superconductors, and suggest possible experimental tests of this theory.

Chern-Simons term by spontaneous symmetry breaking in an abelian Higgs model

We show that the Chern-Simons terms can be generated by spontaneous symmetry breaking in a generalized abelian Higgs model in 2 + 1 dimensions. We analyze this model in some detail and show the existence of two (neutral) vortices of finite energy in each topologically nontrivial sector.

Possible existence of topological excitations in quantum spin models in low dimensions

The possibility of existence of topological excitations in the anisotropic quantum Heisenberg model in one and two spatial dimensions is studied using coherent state method. It is found that a part of the Wess-Zumino term contributes to the partition function, as a topological term for ferromagnets in the long wavelength limit in both one and two dimensions. In particular, the XY limit of the two-dimensional anisotropic ferromagnet is shown to retain the topological excitations, as expected from the quantum Kosterlitz-Thouless scenario.

EFFECTIVE THEORY FOR A QUANTUM SPIN SYSTEM IN LOW DIMENSIONS – BEYOND THE LONG WAVELENGTH LIMIT

An effective theory for a quantum spin system in low dimensions is constructed in the finite-q regime. It is shown that there are field configurations for which Wess–Zumino terms contribute to the partition functions as topological terms for ferromagnets as well as antiferromagnets in both one- and two-dimensional lattices. This is in sharp contrast to the absence of topological excitations in two-dimensional quantum antiferromagnets in the long wavelength limit.

N = 2 super W∞ algebra and its nonlinear realization through super KP formulation

Abstract A nonlinear realizations of super W∞ algebra is shown to exist through a consistent superLax formulation of super KP hierarchy. The reduction of the superLax operator gives rise to the Lax operators for N = 2 generalized super KdV hierarchies, proposed by Inami and Kanno. The Lax equations are shown to be Hamiltonian and the associated Poisson bracket algebra among the superfields, consequently, gives rise to a realization of nonlinear super W∞ algebra.

Physical realization and possible identification of topological excitations in quantum Heisenberg anti-ferromagnet on a two dimensional lattice

Physical spin configurations corresponding to topological excitations, expected to be present in the XY limit of a quantum spin 1/2 Heisenberg anti-ferromagnet, are probed on a two dimensional square lattice. Quantum vortices (anti-vortices) are constructed in terms of coherent staggered spin field components, as limiting case of meronic (anti-meronic) configurations. The crucial role of the associated Wess-Zumino-like (WZ-like) term is highlighted in our procedure. The time evolution equation of coherent spin fields used in this analysis is obtained by applying variational principle on the quantum Euclidean action corresponding to the Heisenberg anti-ferromagnet on lattice. It is shown that the WZ-like term can distinguish between vortices and anti-vortices only in a charge sector with odd topological charges. Our formalism is distinctly different from the conventional approach for the construction of quantum vortices (anti-vortices).

Topological Excitations in Quantum Spin Systems

The origin and significance of topological excitations in quantum spin models in low dimensions are presented in detail. Besides a general review, our own work in this area is described in great depth. Apart from theoretical analysis of the existence and properties of spin vortices and antivortices, the possible experimental consequences and signatures are also highlighted. In particular, the distinguishing features between the even and odd charged topological excitations are brought out through a detailed analysis of the topological term in the quantum action. Moreover, an interesting symmetry property is predicted between the excitations from a ferromagnetic model and an antiferromagnetic model. Through a novel approach of ours, a bridge is established between field theoretical formalism and the well-known statistical mechanical treatment of Berezinskii-Kosterlitz-Thouless (BKT) transition involving these topological excitations. Furthermore, a detailed phenomenological analysis of the experimentally observed static and dynamic magnetic properties of the layered magnetic materials, possessing XY anisotropy in the in-plane spin-spin couplings, is undertaken to test the theoretical predictions regarding the behaviour of these excitations. The importance and the crucial role of quantum spin fluctuations in these studies are also brought out very clearly by our analysis.

Consistent 3D Quantum gravity on Lens Spaces

AbstractWe study non-perturbative quantization of 3d gravity with positive cosmological constant (de Sitterspace being the prototype vacuum solution, whose Euclideanization of course gives the three sphere) onthe background topology of lens space, which is a three spheres modulo a discrete group. Instead of thestrategy followed by a recent work [1], which compares results in the second and first order formulationsof gravity, we concentrate on the later solely. We note, as a striking feature, that the quantization, thatrelies heavily on the axiomatics of topological quantum field theory (TQFT) can only be consistentlycarried by augmenting the conventional theory by an additional topological term coupled through adimensionless parameter. More importantly the introduction of this additional parameter renders thetheory finite. 1 Introduction Most of the non-trivial results in 3d gravity including the famous BTZ black hole solution is known when thecosmological constant is negative. Also there has been a definite trace of AdS/CFT correspondence whenthe space-time is asymptotically AdS. On the other hand the positive cosmological constant counterpartcan lead to an exact evaluation of the partition function on certain space-time toplogies and has generatedconsiderable interest lately [1]. This is in the light of 1-loop evaluation of 3d gravity partition function andcomparing it with results derived in the context of pure SU(2) Chern-Simons theory formulation [2]. In thisconnection topologically massive gravity (TMG), which unlike pure gravity consists of propagating modes,has been thoroughly studied in [3]. The main question these studies aim to address is whether one can makesense of 3d de Sitter quantum gravity. Surprisingly enough, the pure topological gravity theory fails to giveany satisfactory answer to it in the sense that the partition function (both in one loop and nonperturbativecomputations) tend to diverge unregularizably when one considers sum over lens space geometries; whereasthe answer for TMG containing local degrees of freedom is in the affirmative in the sense that it is tameunder sum over topologies.The pure gravity and TMG calculations have been considered in the Euclidean signature with the moti-vation that Eucldeanized de Sitter gravity is ‘thermal’. This is made precise in terms of the well knownHartle-Hawking state in [1]. Besides, in the Einstein-Hilbert theory path integral is sensible only in the Eu-clidean picture, as in flat background quantum field theories. On the other hand if one prefers to study thetheory in first order formulation, in the Chern-Simons (CS) framework, Euclideanization is not an obviousidea that one should come across. This is because CS theory being manifestly topological doesn’t rely onbackground metric as long as perturbative analysis remains not as the primary goal.But once one tries tomake contact with gravity through he