Abstract. We show that the BRST/anti-BRST invariant 3 + 1 dimensional 2-form gauge theory has further nilpotent symmetries (dual BRST /anti-dual BRST) that leave the gauge fixing term invariant. The generator for the dual BRST symmetry is analogous to the coexterior derivative of differential geometry. There exists a bosonic symmetry which keeps the ghost terms invariant and it turns out to be the analogue of the Laplacian operator. The Hodge duality operation is shown to correspond to a discrete symmetry in the theory. The generators of all these continuous symmetries are shown to obey the algebra of the de Rham cohomology operators of differential geometry. We derive the extended BRST algebra constituted by six conserved charges and discuss the Hodge decomposition theorem in the quantum Hilbert space of states. †

We study the noncommutative massless Kalb-Ramond gauge field coupled to a dynamical U (1) gauge field in the adjoint representation together with a compensating vector field. We derive the Seiberg-Witten map and obtain the corresponding mapped action to first order in θ. The (emergent) gravity structure found in other situations is not present here. The off-shell dual scalar theory is derived and it does not coincide with the Seiberg-Witten mapped scalar theory. Dispersion relations are also discussed. The p-form generalization of the Seiberg-Witten map to order θ is also derived.

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We report results of a comprehensive study of the phase transition at T N (~643 K) as a function of particle size in multiferroic BiFeO 3 system. We employed electrical, thermal, and temperature dependent X -ray diffraction (XRD) studies in order to characterize the transition in a host of samples. We also carried out detailed magnetic measurements over a temperature regime 2-300 K under a magnetic field 100-10000 Oe both on bulk and nano-crystalline systems. While in the bulk system a sharp endothermic peak at T N together with a broad feature, ranging over nearly ~150 K (∆T), could be observed in calorimetry, the nanoscale systems exhibit only the broad feature. The characteristic dielectric anomaly, expected at T N , is found to occur both at T O and T N across ∆T in the bulk sample. The Maxwell-Wagner component due to interfaces between heterogenous regions with different conductivities is also present. The magnetic properties, measured at lower temperature, corroborate our observations in calorimetry. The metastability increases in the nanoscale BiFeO 3 with divergence between zero-field cooled (ZFC) and field cooled (FC) magnetization below ~100 K and faster magnetic relaxation. Interestingly, in nanoscale BiFeO 3 , one also observes finite coercivity at lower temperature which points out that suitable design of particle size and shape may induce ferromagnetism. The inhomogeneous distribution of Bi/Fe-ions and/or oxygen nonstoichiometry seems to be giving rise to broad features in thermal, magnetic as well as in electrical responses.

We construct dual formulation of linearised gravity in first order tetrad formalism in arbitrary dimensions within the path integral framework following the standard duality algorithm making use of the global shift symmetry of the tetrad field. The dual partition function is in terms of the (mixed symmetric) tensor field Φ [ν1ν2···ν d−3 ]ν in frame-like formulation. We obtain in d-dimensions the dual Lagrangian in a closed form in terms of field strength of the dual frame-like field. Next by coupling a source with the (linear) Riemann tensor in d-dimensions, dual generating functional is obtained. Using this an operator mapping between (linear) Riemann tensor and Riemann tensor corresponding to the dual field is derived and we also discuss the exchange of equations of motion and Bianchi identity.

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We study the relationship between three non-Abelian topologically massive gauge theories, viz. the naïve non-Abelian generalization of the Abelian model, Freedman-Townsend model and the dynamical 2-form theory, in the canonical framework. Hamiltonian formulation of the naïve 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 naïve non-Abelian model. The reducibility aspect and gauge algebra of the latter models are also discussed.