We consider properties of a covariant worldvolume action for a system of N coincident Dp– branes in D=(p+2) dimensional space–time (so called codimension one branes). In the case of N coincident D0–branes in D=2 we then find a generalization of this action to a model which includes fermionic degrees of freedom and is invariant under target–space supersymmetry and worldline kappa–symmetry. We fi...

In this paper we revisit the isomorphism SU(2) ⊗ SU(2) ∼= SO(4) to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix Q by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold SU(2n)/SO(2n) which characterizes entanglements i...

Transformation groupoids associated to group actions capture the interplay between global and local symmetries of structures described in set-theoretic terms. This paper examines the analogous situation for structures described in categorytheoretic terms, where symmetry is expressed as the action of a 2-group G (equivalently, a categorical group) on a category C. It describes the construction o...

We compute the one-loop holomorphic effective action of the massless Cartan sector of N = 2 SYM theory in the Coulomb branch, taking into account the contributions both from the charged hypermultiplets and off-diagonal components of the gauge superfield. We use the manifestly supersymmetric harmonic superfields diagram techniques adapted to N = 2 supersymmetry with the central charges induced b...

We study homoclinic points of non-expansive automorphisms of compact abelian groups. Connections between the existence of non-trivial homoclinic points, expansiveness, entropy and adjoint automorphisms (in the sense of Einsiedler and Schmidt) are explored. Some implications for countable abelian group actions by automorphisms of compact abelian groups are also considered and it is shown that if...

In this paper we revisit the isomorphism SU(2) ⊗ SU(2) ∼= SO(4) to apply to some subjects in Quantum Computation and Mathematical Physics. The unitary matrix Q by Makhlin giving the isomorphism as an adjoint action is studied and generalized from a different point of view. Some problems are also presented. In particular, the homogeneous manifold SU(2n)/SO(2n) which characterizes entanglements i...

We compute the effective action in terms of the Polyakov loop for the 3dimensional pure fundamental-adjoint SU(2) lattice gauge theory at nonzero temperatures using the strong coupling expansion. In the extended coupling plane we show the existence of a tricritical point where the nature of the deconfinement transition undergoes a change from second to first order. The resulting phase structure...

We prove a pair of transformations relating elliptic hypergeometric integrals of different dimensions, corresponding to the root systems BCn and An; as a special case, we recover some integral identities conjectured by van Diejen and Spiridonov. For BCn, we also consider their “Type II” integral. Their proof of that integral, together with our transformation, gives rise to pairs of adjoint inte...

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W , we show that the Chevalley morphism π : t/W → g/G is an isomorphism except for the group Sp2n over a base with 2-torsion...

we give some sufficient conditions under which the tuple of the adjoint of weighted composition operators $(c_{omega_1,varphi_1}^*‎ , ‎c_{omega_2,varphi_2}^*)$ on the hilbert space $mathcal{h}$ of analytic functions is supercyclic‎.