The quenched approximation in some two-dimensional field theories

We investigate the effect of suppressing closed fermion loops (the quenched approximation) in some (1 + 1)-dimensional field theories. In the Schwinger and Thirring models we find that effects of fermion loops on bound state masses can be absorbed in a rescaling of the coupling constant. In the Schwinger model an extra (decoupled) massless ghost appears and the order parameter $\text{〈}\text{ψ}\text{ψ〉}$ becomes infrared divergent. In an extension of the Schwinger model we compute effective lagrangians for the bound state spectrum in the quenched and unquenched case that look rather different.     

Non-perturbative renormalization group for field theories with scalars and fermions

An approximate, but non-perturbative, RG equation is derived for theories involving scalars and fermions, ind dimensions withn _f flavours. The approximation consists in restricting the parameter space to interactions without derivatives. In a numerical study of the equation ind=3 andd=4, in the range of parameter space explored, no evidence is found of new fixed points generated by the inclusion of fermions.     

Batalin-Vilkovisky algebras and two-dimensional topological field theories

By a Batalin-Vilkovisky algebra, we mean a graded commutative algebraA, together with an operator :A A ₊₁ such that ² = 0, and [,a]–a is a graded derivation ofA for allaA. In this article, we show that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions. We make use of a technique from algebraic topology: the theory of operads.The author is partially supported by a fellowship of the Sloan Foundation and a research grant of the NSF     

Wilson renormalization group formulation of real time thermal field theories

We apply Renormalization Group techniques to the Real Time formulation of thermal field theory. Due to the separation between the T = 0 and the T ≠ 0 parts of the propagator in this formalism, one can derive exact evolution equations for the Green functions describing the effect of integrating out thermal fluctuations of increasing wavelengths, the initial conditions being the renormalized Green functions of the T = 0 theory. As a first application, we study the phase transition for the real scalar theory, computing the order of the transition, the critical temperature, and critical exponents, in different approximations to the evolution equations for the scalar potential.     

Strings on pp-waves and massive two-dimensional field theories

We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet Lagrangian is that of an interacting massive field theory. When the light cone Lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the worldsheet. We consider situations with both flat and curved transverse spaces. We describe in some detail the background giving rise to the N=2 sine Gordon theory on the worldsheet. Massive mirror symmetry relates it to the deformed CP¹ model (or sausage model) which seems to elude a purely supergravity target space interpretation. To cite this article: J. Maldacena, L. Maoz, C. R. Physique 4 (2003).     

Real-space renormalization group study of a two-dimensional nonlinear massless field

The magnetic susceptibility of CuF₂·2H₂O has been measured as a function of magnetic field from 1.5 to 10 K. The spin-flop transition was observed and its value extrapolated to zero temperature is H_SF(0) = 30.5 kOe. This critical field is in very good agreement with data obtained from zero field measurements.     

Relativity,noncommutative geometry,renormalization and particle physics

A. Connes and A. Chamseddine have proposed a new geometric version of the standard model including a noncommutative relativity action. We present a systematic analysis of the relations among masses and coupling constants in these approaches. At the tree level, for a given top mass, the Higgs mass m_H is constrained to lie in an interval. Moreover, playing with the noncommutative gauge couplings, we compare the influence of the Higgs mass renormalization in these effective theories. The existing intersection is m_H = 188–201 GeV.     

Homotopy algebra morphism and geometry of classical string field theories

We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background, there are many string field theories corresponding to different decomposition of moduli space of Riemann surfaces. It is shown that any classical open string field theories on a fixed conformal background are A_∞-quasi-isomorphic to each other. This indicates that they have isomorphic moduli space of classical solutions. The minimal model theorem in A_∞-algebras plays a key role in these results. Its natural and geometric realization on formal supermanifolds is also given. The same results hold for classical closed string field theories, whose algebraic structures are governed by L_∞-algebras.     

Multiphonon renormalization of the spectrum of two-dimensional excitons in a magnetic field

The renormalization of the dispersion law for two-dimensional excitons in a magnetic field is studied by the Green's-function method taking into account multiphonon processes.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 3–7, April, 1987.     

A non-Gaussian renormalization group fixed point for hierarchical scalar lattice field theories

A rigorous method is developed to handle the large field problems in the Wilson-Kadanoff renormalization group approach to critical lattice systems of unbounded spins. We use this method to study in a hierarchical approximation the non-Gaussian renormalization group fixed point which governs the infrared behaviour of critical lattice field theories in three dimensions. The method is an improvement of the analyticity techniques of Gawedzki and Kupiainen: using Borel summation techniques we are able to incorporate the large field region into the perturbative region so that the theory is completely described in terms of convergent expansions.Supported in part by the National Science Foundation under Grant No. DMS-8540879Supported in part by the National Science Foundation under Grant No. DMR81-14726Part of this work has been carried out during a visit of the author at the Courant Institute of Mathematical Sciences, NYU     

The geometry of Ingarden spaces

The Randers spaces RFⁿ were introduced by R. S. Ingarden. They are considered as Finsler spaces Fⁿ = (M, α + β) equipped with the Cartan nonlinear connection. In the present paper we define and study what we call the Ingarden spaces, I Fⁿ, as Finsler spaces I Fⁿ = (M, α + β) equipped with the Lorentz nonlinear connection. The spaces R Fⁿ and I Fⁿ are completely different. For I Fⁿ we discuss: the variational problem, Lorentz nonlinear connection, canonical N-metrical connection and its structure equations, the Cartan 1-form ω, the electromagnetic 2-form tF and the almost symplectic 2-form 0. The formula dω = F+θ is established. It has as a consequence the generalized Maxwell equations. Finally, the almost Hermitian model of I Fⁿ is constructed.     

The use of dimensional renormalization schemes in unified theories

We present details and clarify some points in a recently proposed modification of the minimal subtraction adapted to unified theories. As an application we give a precise value of the superheavy gauge boson masses in SU(5).     

Constraints on two-dimensional conformal field theories from knot invariants

The connection between Witten's topological three-dimensional gauge theory and RCFTs provides a natural setting to study the interplay between surface diffeomorphisms and intertwining of Wilson loops. These considerations lead directly to constraints on RFCTs including those previously derived by Vafa.