Conformally invariant gauge fixed actions for 2-D topological gravity

We show that invariants of Mumford for moduli spaces of curves are obtainable from a gauge fixed action of a topological quantum field theory in two dimensions. The method is completely analogous to the relation of Donaldson invariants with the topological quantum field theory for gauge theories in four dimensions.Supported by D.O.E. Grant DE-FG02-88ER 25066     

Canonical quantization of general relativity in discrete space-times

It has long been recognized that lattice gauge theory formulations, when applied to general relativity, conflict with the invariance of the theory under diffeomorphisms. We analyze discrete lattice general relativity and develop a canonical formalism that allows one to treat constrained theories in Lorentzian signature space-times. The presence of the lattice introduces a "dynamical gauge" fixing that makes the quantization of the theories conceptually clear, albeit computationally involved. The problem of a consistent algebra of constraints is automatically solved in our approach. The approach works successfully in other field theories as well, including topological theories. A simple cosmological application exhibits quantum elimination of the singularity at the big bang.     

A delicate universe: compactification obstacles to D-brane inflation

We investigate whether explicit models of warped D-brane inflation are possible in string compactifications. To this end, we study the potential for D3-brane motion in a warped conifold that includes holomorphically embedded D7-branes involved in moduli stabilization. The presence of the D7-branes significantly modifies the inflaton potential. We construct an example based on a very simple and symmetric embedding due to Kuperstein, z1= const, in which it is possible to fine-tune the potential so that slow-roll inflation can occur. The resulting model is rather delicate: inflation occurs in the vicinity of an inflection point, and the cosmological predictions are extremely sensitive to the precise shape of the potential.     

Successful supersymmetric inflation

We reconsider the problems of cosmological inflation in effective supergravity theories. A singlet field in a hidden sector is demonstrated to yield an acceptable inflationary potential, without fine tuning. In the simplest such model, the requirement of generating the microwave background anisotropy measured by COBE fixes the inflationary scale to be about 10¹⁴ GeV, implying a reheat temperature of order 10⁵ GeV. This is low enough to solve gravitino problem but high enough to allow baryogenesis after inflation. Such consistency requires that the generation of gravitational waves be negligible and that the spectrum of scalar density perturbations depart significantly from scale invariance, thus improving the fit to large-scale structure in an universe dominated by cold dark matter. We also consider the problems associated with gravitino production through inflaton decay and with other weakly coupled fields such as the moduli encountered in (compactified) string theories.     

parafermionic current algebras of torus/orbifold models

We study the quantum field theory of bosons on the torus and the orbifold. When the torus is in special moduli, the representations of the theory are equivalent to those of some rational conformal field theories. We show that there are parafermonic current algebras in Z_N orbifold models.     

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U(N_c) and SU(N_c) with N _f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.     

Algebraic-geometrical formulation of two-dimensional quantum gravity

We find a volume form on moduli space of double-punctured Riemann surfaces whose integral satisfies the Painlevé I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic expansion of the specific heat as an integral on an infinite-dimensional moduli space in the spirit of the Friedan-Shenker approach. We outline a conjectural derivation of such recursion relations using the Duistermaat-Heckman theorem.Partly supported by the European Community Research Programme Gauge theories, applied supersymmetry and quantum gravity, contract SC1-CT92-0789     

Semi-Classical Quantum Fields Theories and Frobenius Manifolds

We show that a semi-classical quantum field theory comes with a versal family with the property that the corresponding partition function generates all path integrals., satisfies a system of second order differential equations determined by algebras of classical observables. This versal family gives rise to a notion of special coordinates that is analogous to that in string theories. We also show that for a large class of semi-classical theories, their moduli space has the structure of a Frobenius super-manifold. This work was supported by KOSEF Interdisciplinary Research Grant No. R01-2006-000-10638-0.     

Quintessential inflation at low reheating temperatures

We have tested some simple quintessential inflation models, imposing the requirement that they match with the recent observational data provided by the BICEP and Planck team and leading to a reheating temperature, which is obtained via gravitational particle production after inflation, supporting the nucleosynthesis success. Moreover, for the models coming from supergravity one needs to demand low temperatures in order to avoid problems such as the gravitino overproduction or the gravitational production of moduli fields, which are obtained only when the reheating temperature is due to the production of massless particles with a coupling constant very close to its conformal value.     

Background Dynamics of Pre-inflationary Scenario in Brans-Dicke Loop Quantum Cosmology

Recently the background independent nonperturbative quantization has been extended to various theories of gravity and the corresponding quantum effective cosmology has been derived, which provides us with necessary avenue to explore the pre-inflationary dynamics. Brans-Dicke (BD) loop quantum cosmology (LQC) is one of such theories whose effective background dynamics is considered in this article. Starting with a quantum bounce, we explore the pre-inflationary dynamics of a universe sourced by a scalar field with the Starobinsky potential in BD-LQC. Our study is based on the idea that though Einstein's and Jordan's frames are classically equivalent up to a conformal transformation in BD theory, this is no longer true after quantization. Taking the Jordan frame as the physical one we explore in detail the bouncing scenario which is followed by a phase of a slow roll inflation. The three phases of the evolution of the universe, namely, bouncing, transition from quantum bounce to classical universe, and the slow roll inflation, are noted for an initially kinetic energy dominated bounce. In addition, to be consistent with observations, we also identify the allowed phase space of initial conditions that would produce at least 60 e-folds of expansion during the slow roll inflation.     

Nonthermal fixed points: effective weak coupling for strongly correlated systems far from equilibrium

Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The nonthermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early Universe after inflation and the question of fast thermalization in heavy-ion collision experiments.     

Notes on generalized global symmetries in QFT

It was recently argued that quantum field theories possess one‐form and higher‐form symmetries, labelled ‘generalized global symmetries.’ In this paper, we describe how those higher‐form symmetries can be understood mathematically as special cases of more general 2‐groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one‐form and higher‐form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli ‘space’ (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2‐group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.     

The kinematics of cosmic reheating

We calculate the relaxation rate of a scalar field in a plasma of other scalars and fermions with gauge interactions using thermal quantum field theory. It yields the rate of cosmic reheating and thereby determines the temperature of the “hot big bang” in inflationary cosmology. The total rate originates from various processes, including decays and inverse decays as well as Landau damping by scatterings. It involves quantum statistical effects and off-shell transport. Its temperature dependence can be highly non-trivial, making it impossible to express the reheating temperature in terms of the model parameters in a simple way. We pay special attention to the temperature dependence of the phase space due to the modified dispersion relations in the plasma. We find that it can have a drastic effect on the efficiency of perturbative reheating, which depends on the way particles in the primordial plasma interact. For some interactions thermal masses can effectively close the phase space for the dominant dissipative processes and thereby impose an upper bound on the reheating temperature. In other cases they open up new channels of dissipation, hence increase the reheating temperature. At high temperatures we find that the universe can even be heated through couplings to fermions, which are often assumed to be negligible due to Pauli-blocking. These effects may also be relevant for baryogenesis, dark matter production, the fate of moduli and in scenarios of warm inflation.     

A remark on quantum corrections to classical confinement

We discuss some simple models related to quantum corrections of the MIT-bag in the framework of local field theories in two space-time dimensions. A recent result due to A. Chodos and A. Klein is generalized. We find that the corresponding quantum field theories become free or have an energy spectrum unbounded from below.     

Boundary Conditions for Topological Quantum Field Theories,Anomalies and Projective Modular Functors

We study boundary conditions for extended topological quantum field theories (TQFTs) and their relation to topological anomalies. We introduce the notion of TQFTs with moduli level m, and describe extended anomalous theories as natural transformations of invertible field theories of this type. We show how in such a framework anomalous theories give rise naturally to homotopy fixed points for n-characters on ∞-groups. By using dimensional reduction on manifolds with boundaries, we show how boundary conditions for n + 1-dimensional TQFTs produce n-dimensional anomalous field theories. Finally, we analyse the case of fully extended TQFTs, and show that any fully extended anomalous theory produces a suitable boundary condition for the anomaly field theory.     

Dimensional Reduction Over the Quantum Sphere and Non-Abelian q-Vortices

We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a K?hler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural action of the quantum group SU _q (2), and also of invariant gauge connections on these bundles. The reduction of Yang–Mills gauge theory on the product space leads to a q-deformation of the usual quiver gauge theories on M. We formulate generalized instanton equations on the quantum space and show that they correspond to q-deformations of the usual holomorphic quiver chain vortex equations on M. We study some topological stability conditions for the existence of solutions to these equations, and demonstrate that the corresponding vacuum moduli spaces are generally better behaved than their undeformed counterparts, but much more constrained by the q-deformation. We work out several explicit examples, including new examples of non-abelian vortices on Riemann surfaces, and q-deformations of instantons whose moduli spaces admit the standard hyper-K?hler quotient construction.     

Topological phases of quantum theories. Chern-Simons theory

We analyze the vacuum structure (degeneracy, nodes and symmetries) of some quantum theories with special emphasis on the study of its dependence on the geometry and topology of the classical configuration space. The study of the topological limit shows that many low energy properties of those quantum theories can be inferred from the structure of their topological phases. After reviewing some simple pure quantum mechanical models (planar rotor, magnetic monopole and quantum Hall effect) we focus on the study of the rich relationship existing between topologically massive gauge theories and their topological phases, Chern-Simons theories. In particular we show that, although in a finite volume the degeneracy of the quantum vacuum of gauge theories depends on the topology of the underlying Riemann surface, in an infinite volume the vacuum is unique. Finally, the topological structure of Chern-Simons theory is analyzed in a covariant formalism within a geometric regularization scheme. We discuss in some detail the structure of the different metric dependent contributions to the Chern-Simons partition function and the associated topological invariants.     

Collective coordinates in Fermi systems

The problem of developing a consistent perturbation theory for a Fermi system in the case in which the unperturbed system exhibits dynamical symmetry breaking is discussed, by using collective coordinate methods. By adapting to this problem the methods used in the quantization of gauge theories, it is shown how to deal with composite zero-frequency excitations in such a way that the resulting perturbation theory is free of infrared divergencies. Explicit calculations are carried out in the case of a simple quantum mechanical model representing a superfluid Fermi system.