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We use geometric algebra techniques to give a synthetic and computationally efficient approach to Fierz identities in arbitrary dimensions and signatures, thus generalizing previous work. Our approach leads to a formulation which displays the underlying real, complex or quaternionic structure in an explicit and conceptually clear manner and is amenable to implementation in various symbolic computation systems. We illustrate our methods and results with a few examples which display the basic features of the three classes of pin representations governing the structure of such identities in various dimensions and signatures.
We use the AdS/CFT correspondence in a regime in which the field theory reduces to fluid dynamics to construct an infinite class of new black objects in Scherk-Schwarz compactified AdS(d+2) space. Our configurations are dual to black objects that gen
We present a short review of the action and coaction of Hopf algebras on Clifford algebras as an introduction to physically meaningful examples. Some q-deformed Clifford algebras are studied from this context and conclusions are derived.
We investigate symmetry breaking in two-dimensional field theories which have a holographic gravity dual. Being at large N, the Coleman theorem does not hold and Goldstone bosons are expected. We consider the minimal setup to describe a conserved cur
Using the techniques developed in arxiv: 1203.3544 we compute the universal part of the equilibrium partition function characteristic of a theory with multiple abelian U(1) anomalies in arbitrary even spacetime dimensions. This contribution is closel
Exact analytic solutions of static, stable, non-planar BPS domain wall junctions are obtained in extended Abelian-Higgs models in $(D+1)$-dimensional spacetime. For specific choice of mass parameters, the Lagrangian is invariant under the symmetric g