Gauge models in modified triplectic quantization (Q2772949)

Two of the authors and Gitman proposed the modified triplectic quantization [\textit{B. Geyer}, \textit{M. Gitman} and \textit{P. M. Lavrov}, Mod. Phys. Lett. A 14, 661-670 (1999) hereafter refered to as [1]]. In this paper, this quantization is applied to the Freedman-Townsend model of non-Abelian antisymmetric tensor fields, \(W_2\) gravity and 2D gravity with dynamical torsion. For these models, by using explicit solutions of generating equations, the vacuum functionals are constructed and the \(\text{Sp}(2)\)-invariant effective actions are determined. The corresponding transformations of the extended BRST symmetry are also obtained.NEWLINENEWLINENEWLINEThe method of \(\text{Sp}(2)\)-covariant quantization [\textit{I. A. Batalin}, \textit{P. M. Lavrov} and \textit{I. M. Tyutin}, J. Math. Phys. 31, 1487-1493 (1990; Zbl 0716.58035); ibid. 32, No. 2, 532-539 (1991; Zbl 0825.58063); ibid. 32, 2513-2521 (1991)] provides a realization of the extended BRST symmetry for general gauge theories. In the framework of the triplectic quantization [\textit{I. A. Batalin} and \textit{R. Marnelius}, Nucl. Phys. B 456, 521-539 (1996; Zbl 1002.81562)], the gauge-fixing part of the action in the functional integral is determined by generating equations formally similar to the equations that describe the quantum action. In [1], the system of generating equations is modified so that the classical action of a theory satisifes (in the limit \(\hbar\to 0\)) the generating equations for the quantum action \(W= W(\phi,\phi^*, \pi,\overline\phi)\), NEWLINE\[NEWLINE{1\over 2} (W, W)^a+ V^a W= i\hbar \Delta^a W.NEWLINE\]NEWLINE In the introduction, the generating equations for the gauge-fixing functional and vacuum functional of the modified triplectic formalism are also presented. In Sect. 2, the Freedman-Townsend model is investigated. This model is described by the action NEWLINE\[NEWLINES_{\text{cl}}(A^p_\mu, H^p_{\mu\nu})= \int d^4x\Biggl(-{1\over 4} \varepsilon^{\mu\nu\rho\sigma} F^p_{\mu\nu} H^p_{\rho\sigma}+ {1\over 2} A^p_\mu A^{p\mu}\Biggr).NEWLINE\]NEWLINE After giving explicit solution of generating equations and list up symmetry transformations by which the vacuum functional is invariant, the vacuum functional \(Z\) is represented as an integral over the fields \(\phi^A\) of the complete configuration space. It shows the unitarity of the physical \(S\) matrix. \(W_2\)-gravity and 2D gravity with dynamical torsion are treated in Sect. 3 and 4, and it is shown that effective action takes the form NEWLINE\[NEWLINES_{\text{eff}}= S_{\text{cl}}+{1\over 2} \varepsilon_{ab} s^b s^a F(\phi, h),NEWLINE\]NEWLINE in both cases. Here \(s^a\) in the action of the (anti)BRST operator onto the fields \(\phi^A\) according to the rule \(\delta\phi^A= (s^a\phi^A)\mu_a\). Possible anomalies which occur if loop correction are taken into account are not determined.