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arXiv:hep-th/0003192v2 4 Apr 2000
Freedman-Townsend vertex from Hamiltonian BRST cohomology
C. Bizdadea∗ , E. M. Cioroianu, S. O. Saliu† Department of Physics, University of Craiova 13 A. I. Cuza Str., Craiova RO-1100, Romania February 1, 2008
Abstract Consistent interactions among a set of two-form gauge ﬁelds in four dimensions are derived along a Hamiltonian cohomological procedure. It is shown that the deformation of the BRST charge and BRST-invariant Hamiltonian for the free model leads to the FreedmanTownsend interaction vertex. The resulting interaction deforms both the gauge transformations and reducibility relations, but not the algebra of gauge transformations. PACS number: 11.10.Ef
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Introduction
The cohomological understanding of the antiﬁeld-BRST symmetry [1]–[2] was proved to be a useful tool for constructing consistent interactions in gauge theories [3]–[6]. Among the models of great interest in theoretical physics that have been inferred along the deformation of the master equation, we mention the Yang-Mills theory [7], the Freedman-Townsend model [8], and the Chapline-Manton model [9]. Also, it is important to notice the
∗ †
e-mail addresses: bizdadea@central.ucv.ro and bizdadea@hotmail.com e-mail addresses: osaliu@central.ucv.ro and odile saliu@hotmail.com
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deformation results connected to Einstein’s gravity theory [10] and four- and eleven-dimensional supergravity [11]. Recently, ﬁrst-order consistent interactions among exterior p-forms have been approached in [12] also by means of the antiﬁeld-BRST formulation. On the one hand, models with p-form gauge ﬁelds (antisymmetric tensor ﬁelds of various ranks) play an important role in string and superstring theory, supergravity and the gauge theory of gravity [13]–[16]. The study of theoretical models with gauge antisymmetric tensor ﬁelds give an example of so-called ‘topological ﬁeld theory’ and lead to the appearance of topological invariants, being thus in close relation to space-time topology, hence with lower dimensional quantum gravity [14]. In the meantime, antisymmetric tensor ﬁelds of various orders are included within the supergravity multiplets of many supergravity theories [15], especially in 10 or 11 dimensions. The construction of ‘dual’ Lagrangians involving p-forms is naturally involved with General Relativity and supergravity in order to render manifest the SL (2, R) symmetry group of stationary solutions of Einstein’s vacuum equation, respectively to reveal some subtleties of ‘exact solutions’ for supergravity [16]. On the other hand, the Hamiltonian version of BRST formalism [17], [2] appears to be the most natural setting for implementing the BRST symmetry in quantum mechanics [2] (Chapter 14), as well as for establishing a proper connection with canonical quantization formalisms, like, for instance, the reduced phasespace or Dirac quantization procedures [18]. These considerations motivate the necessity o