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Register a new userOn the quantisation and anomalies of antisymmetric tensor-spinors
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We perform the quantisation of antisymmetric tensor-spinors (fermionic $p$-forms) $psi^alpha_{mu_1 dots mu_p}$ using the Batalin-Vilkovisky field-antifield formalism. Just as for the gravitino ($p=1$), an extra propagating Nielsen-Kallosh ghost appears in quadratic gauges containing a differential operator. The appearance of this `third ghost is described within the BV formalism for arbitrary reducible gauge theories. We then use the resulting spectrum of ghosts and the Atiyah-Singer index theorem to compute gravitational anomalies.
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This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three dimensional string-like structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented; while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is show how the Lax pair of the integrable nonlinear Schroedinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation and it is described how a spinor based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schroedinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauss-Godazzi equation that describes surfaces in three dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two dimensional and four dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two dimensional integrable models as embedded structures in the four dimensional decomposed SU(2) Yang-Mills theory are presented.
We study the zero mode cohomology of the sum of two pure spinors. The knowledge of this cohomology allows us to better understand the structure of the massless vertex operator of the Type IIB pure spinor superstring.
We investigate a non-trivial extension of the $D-$dimensional Poincare algebra. Matrix representations are obtained. The bosonic multiplets contain antisymmetric tensor fields. It turns out that this symmetry acts in a natural geometric way on these $p-$forms. Some field theoretical aspects of this symmetry are studied and invariant Lagrangians are explicitly given.
This paper studies the space of $L ^2 $ harmonic forms and $L ^2 $ harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find a 2-parameter family of $L ^2 $ zero modes of the Dirac operator twisted by an arbitrary $L ^2 $ harmonic connection. We also show that the number of zero modes found is equal to the index of the Dirac operator. We compare our results with those known in the case of Taub-NUT and Euclidean Schwarzschild as these manifolds present interesting similarities with Taub-bolt. In doing so, we slightly generalise known results on harmonic spinors on Euclidean Schwarzschild.
We investigate the Kalb-Ramond antisymmetric tensor field as solution to the muon $g-2$ problem. In particular we calculate the lowest-order Kalb-Ramond contribution to the muon anomalous magnetic moment and find that we can fit the new experimental value for the anomaly by adjusting the coupling without affecting the electron anomalous magnetic moment results.
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