A Functional and Lagrangian Formulation of Two-Dimensional Topological Gravity

We reconsider two-dimensional topological gravity in a functional and lagrangian framework. We derive its Slavnov-Taylor identities and discuss its (in)dependence on the background gauge. Correlators of reparamerization invariant observables are shown to be globally defined forms on moduli space. The potential obstruction to their gauge-independence is the non-triviality of the line bundle on moduli space ${\cal L}_x$, whose first Chern-class is associated to the topological invariants of Mumford, Morita and Miller. Based on talks given at the Fubini Fest, Torino, 24-26 February 1994, and at the Workshop on String Theory, Trieste, 20-22 April 1994.Comment: 11 pages, harvmac, CERN-TH-7302/94, GEF-Th-6/199

Chiral QED in Terms of Chiral Boson with a Generalized Fadeevian Regularization

Chiral QED with a generalized Fadeevian regularization is considered. Imposing a chiral constraint a gauged version of Floranini-Jackiw lagrangian is constructed. The imposition of the chiral constarint has spoiled t he manifestly Lorentz covariance of the theory. The phase space structure for this theory has been det ermined. It is found that spectrum changes drastically but it is Lorentz invariant. Chiral fermion di sappears from the spectra and the photon anquire mass as well. Poincare algebra has been calculated to show physicial Lorentz invariance explicitely.Comment: 11 page

The Renormalization of Non-Commutative Field Theories in the Limit of Large Non-Commutativity

We show that renormalized non-commutative scalar field theories do not reduce to their planar sector in the limit of large non-commutativity. This follows from the fact that the RG equation of the Wilson-Polchinski type which describes the genus zero sector of non-commutative field theories couples generic planar amplitudes with non-planar amplitudes at exceptional values of the external momenta. We prove that the renormalization problem can be consistently restricted to this set of amplitudes. In the resulting renormalized theory non-planar divergences are treated as UV divergences requiring appropriate non-local counterterms. In 4 dimensions the model turns out to have one more relevant (non-planar) coupling than its commutative counterpart. This non-planar coupling is ``evanescent'': although in the massive (but not in the massless) case its contribution to planar amplitudes vanishes when the floating cut-off equals the renormalization scale, this coupling is needed to make the Wilsonian effective action UV finite at all values of the floating cut-off.Comment: 35 pages, 8 figures; typos correcte

The Kontsevich Connection on the Moduli Space of FZZT Liouville Branes

We point out that insertions of matrix fields in (connected amputated) amplitudes of (generalized) Kontsevich models are given by covariant derivatives with respect to the Kontsevich moduli. This implies that correlators are sections of symmetric products of the (holomorphic) tangent bundle on the (complexified) moduli space of FZZT Liouville branes. We discuss the relation of Kontsevich parametrization of moduli space with that provided by either the (p,1) or the (1,p) boundary conformal field theories. It turns out that the Kontsevich connection captures the contribution of contact terms to open string amplitudes of boundary cosmological constant operators in the (1,p) minimal string models. The curvature of the connection is of type (1,1) and has delta-function singularities at the points in moduli space where Kontsevich kinetic term vanishes. We also outline the extention of our formalism to the c=1 string at self-dual radius and discuss the problems that have to be understood to reconciliate first and second quantized approaches in this case.Comment: 34 pages, 2 eps figures, LaTex; typos corrected (including title); more typos fixed, including those in Eqs.(72) and (132

Physical States at the Tachyonic Vacuum of Open String Field Theory

We illustrate a method for computing the number of physical states of open string theory at the stable tachyonic vacuum in level truncation approximation. The method is based on the analysis of the gauge-fixed open string field theory quadratic action that includes Fadeev-Popov ghost string fields. Computations up to level 9 in the scalar sector are consistent with Sen's conjecture about the absence of physical open string states at the tachyonic vacuum. We also derive a long exact cohomology sequence that relates relative and absolute cohomologies of the BRS operator at the non-perturbative vacuum. We use this exact result in conjunction with our numerical findings to conclude that the higher ghost number non-perturbative BRS cohomologies are non-empty.Comment: 43 pages, 16 eps figures, LaTe

The Wilson-Polchinski Renormalization Group Equation in the Planar Limit

We derive the Wilson-Polchinski RG equation in the planar limit. We explain that the equation necessarily involves also non-planar amplitudes with sphere topology, which represent multi-trace contributions to the effective action. The resulting RG equation turns out to be of the Hamilton-Jacobi type since loop effects manifest themselves through terms which are linear in first order derivatives of the effective action with respect to the sources. We briefly outline applications to renormalization of non-commutative field theories, matrix models with external sources and holography.Comment: 22 pages, Latex, 3 eps figure

On the Semi-Relative Condition for Closed (TOPOLOGICAL) Strings

We provide a simple lagrangian interpretation of the meaning of the $b_0^-$ semi-relative condition in closed string theory. Namely, we show how the semi-relative condition is equivalent to the requirement that physical operators be cohomology classes of the BRS operators acting on the space of local fields {\it covariant} under world-sheet reparametrizations. States trivial in the absolute BRS cohomology but not in the semi-relative one are explicitly seen to correspond to BRS variations of operators which are not globally defined world-sheet tensors. We derive the covariant expressions for the observables of topological gravity. We use them to prove a formula that equates the expectation value of the gravitational descendant of ghost number 4 to the integral over the moduli space of the Weil-Peterson K\"ahler form.Comment: 10 pages, harvmac, CERN-TH-7084/93, GEF-TH-21/199

The Spectrum of Open String Field Theory at the Stable Tachyonic Vacuum

We present a level (10,30) numerical computation of the spectrum of quadratic fluctuations of Open String Field Theory around the tachyonic vacuum, both in the scalar and in the vector sector. Our results are consistent with Sen's conjecture about gauge-triviality of the small excitations. The computation is sufficiently accurate to provide robust evidence for the absence of the photon from the open string spectrum. We also observe that ghost string field propagators develop double poles. We show that this requires non-empty BRST cohomologies at non-standard ghost numbers. We comment about the relations of our results with recent work on the same subject.Comment: 33 pages, 10 figure