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Register a new userCohomology ring of the BRST operator associated to the sum of two pure spinors
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In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.
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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.
The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and some further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to $a^3$. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.
It is well known that the usual formulation of Elko spinor fields leads to a subtle Lorentz symmetry break encoded in the spin sums. Recently it was proposed a redefinition in the dual structure, along with a given mathematical device, which eliminate the Lorentz breaking term in the spin sums. In this work we delve into the analysis of this mathematical device providing a solid framework to the used method.
The details of Lagrangian description of irreducible integer higher-spin representations of the Poincare group with an Young tableaux $Y[hat{s}_1,hat{s}_2]$ having $2$ columns are considered for Bose particles propagated on an arbitrary dimensional Minkowski space-time. The procedure is based, first, on using of an auxiliary Fock space generated by Fermi oscillators (antisymmetric basis), second, on construction of the Verma module and finding auxiliary oscillator realization for $sl(2)oplus sl(2)$ algebra which encodes the second-class operator constraints subsystem in the HS symmetry superalgebra. Application of an BRST-BFV receipt permits to reproduce gauge-invariant Lagrangians with reducible gauge symmetries describing the free dynamics of both massless and massive mixed-antisymmetric bosonic fields of any spin with appropriate number of gauge and Stueckelberg fields. The general prescription possesses by the possibility to derive constrained Lagrangians with only BRST-invariant extended algebraic constraints which describes the Poincare group irreducible representations in terms of mixed-antisymmetric tensor fields with 2 group indices.
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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