On the equivalence between topologically and non-topologically massive abelian gauge theories

We analyse the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are St\"uckelberg formulation of (A) a first order formulation involving one and two form fields, (B) Proca theory, and (C) massive Kalb-Ramond theory. We first quantise these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the Hamiltonian also get mapped. Interestingly it is found that the different NTMGTs are equivalent to different formulations of TMGTs which differ only by a total divergence term. We also provide covariant mappings between the fields in TMGT to NTMGTs at the level of correlation function.Comment: One reference added and a typos corrected. 15 pages, To appear in Mod. Phys. Lett.

Duality of massive gauge invariant theories in arbitrary space-time dimension

We show that dualization of Stueckelberg-like massive gauge theories and $B\wedge F$ models, follows form a general p-dualization of interacting theories in d spacetime dimensions. This is achieved by a particular choice of the external current.Comment: ReVTeX 7pages, no figures, accepted for publ. in Phys.Rev.

Massive Gauge Axion Fields

A gauge invariant formulation for the massive axion is considered. The axion acquires mass through a topological term which couples a (pseudo)scalar and a third rank antisymmetric tensor. Duality, local and canonical equivalences with the non-gauge invariant proposal are established. The supersymmetric version of the gauge invariant model is constructed.Comment: Final version. New references adde

Average Conditional Volatility: A Measure Of Systemic Risk For Commercial Banks

We propose using the cross-sectional (daily) average conditional volatility of commercial bank stock returns as a measure of systemic risk for the U.S. banking industry. The performance of this measure is tested using data from the 2008 pre-crisis period. The measure is shown to incorporate individual bank risk as well as the cumulative riskiness of a cross-section of banks. Cross-sectional regressions indicate that individual bank’s probability of default is unrelated to the bank’s conditional volatility during times of low, industry wide risk (as measured by average conditional volatility). However, the bank’s conditional volatility significantly affects its probability of default when the industry is experiencing a high level risk. Regardless of the industry level risk, a bank’s probability of default has a significant negative relation with its capital adequacy (as measured by the proportion of equity capital). Additionally, at an aggregate level, Granger causality tests indicate that the conditional volatility of ‘big’ banks causes the riskiness of medium and small banks to increase

'Schwinger Model' on the Fuzzy Sphere

In this paper, we construct a model of spinor fields interacting with specific gauge fields on fuzzy sphere and analyze the chiral symmetry of this 'Schwinger model'. In constructing the theory of gauge fields interacting with spinors on fuzzy sphere, we take the approach that the Dirac operator $D_q$ on q-deformed fuzzy sphere $S_{qF}^2$ is the gauged Dirac operator on fuzzy sphere. This introduces interaction between spinors and specific one parameter family of gauge fields. We also show how to express the field strength for this gauge field in terms of the Dirac operators $D_q$ and $D$ alone. Using the path integral method, we have calculated the $2n-$point functions of this model and show that, in general, they do not vanish, reflecting the chiral non-invariance of the partition function.Comment: Minor changes, typos corrected, 18 pages, to appear in Mod. Phys. Lett.

Dual Linearised Gravity in Arbitrary Dimensions

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 $\Phi_{[\nu_{1}\nu_{2}...\nu_{d-3}]\nu}$ in {\it 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.Comment: 14 pages, typos corrected, Published version: Class. Quantum Grav. 22(2005)538