123697695
STRING THEORIES ON RIEMANN SURFACES OF ALGEBRAIC FUNCTIONS
In this paper we extend to a general Riemann surface a formalism used so far for surfaces with Abelian group of symmetry. Using an algebraic equation F(z, w)=0 to define the surface in terms of sheets and branch points, it is possible to construct the correlation functions for b—c systems with integer conformal weight j and for the scalar fields X. Explicit examples are provided for a general surface of genus three and a surface of genus four. No essential complication arises with respect to the hyperelliptic case. At the end we discuss the computation of chiral determinants det using the stress energy tensor method.
119092707
Dirac quantization of the Chern-Simons field theory in the Coulomb gauge
Abstract In this letter the Chern-Simons field theories are studied in the Coulomb gauge using the Dirac's canonical formalism for constrained systems. As a strategy, we first work out the constraints and then quantize, replacing the Dirac brackets with quantum commutators. We find that the Chern-Simons field theories become two dimensional models with no propagation along the time direction. Moreover, we prove that, despite of the presence of non-trivial self-interactions in the gauge fixed functional, the commutation relations between the fields are trivial at any order in perturbation theory in the absence of couplings with matter fields. If these couplings are present, instead, the commutation relations become rather involved, but it is still possible to study their main properties and to show that they vanish at the tree level.
121604245
Performance of the TOTEM neurochip in Higgs search
We present preliminary results on the ability of the neurochip TOTEM to discriminate Higgs particles from background in p-p high energy collisions.
118282052
Toward a Field Theoretical Description of Topologically Linked Polymers
In this work a field theoretical model is constructed to describe the statistical mechanics of an arbitrary number of topologically linked polymers in the context of the analytical approach of Edwards. As an application, the effects of the topological interactions are studied in the one loop approximation. A natural way to include in the treatment also more sophisticated link invariants than the Gauss linking number is outlined.
18373561
Biharmonic conformal field theories
Abstract We construct in this paper a new class of conformal field theories (CFT's) in which the fields are characterized by equations of the biharmonic type. All these theories are interacting and admit an explicit Lagrangian formulation. For that reason, the biharmonic CFT's are useful in the study of interacting CFT's and can have also applications in string theories. Besides, it is possible to interprete the biharmonic CFT's as theories of conformal gravity in two dimensions, which represent an alternative to Liouville field theory.
121244510
On the stochastic quantization of the Chern-Simons theory
Abstract We present in this paper a refined treatment of the stochastic quantization of Chern-Simons field theories. We show in particular that the naive Langevin equation does not lead to a well-defined equilibrium limit. Our main issue is the introduction of a nontrivial kernel in the Langevin equation which yields the correct equilibrium limit. We restrict ourselves to the free field theory case.
119171660
Random geometry, quantum gravity and the Kähler potential
We propose a new method to define theories of random geometries, using an explicit and simple map between metrics and large hermitian matrices. We outline some of the many possible applications of the formalism. For example, a background-independent measure on the space of metrics can be easily constructed from first principles. Our framework suggests the relevance of a new gravitational effective action and we show that it occurs when coupling the massive scalar field to two-dimensional gravity. This yields new types of quantum gravity models generalizing the standard Liouville case.
15521431
On the geometry of super Yang-Mills theories: phases and irreducible polynomials
We study the algebraic and geometric structures that underly the space of vacua of = 1 super Yang-Mills theories at the non-perturbative level. Chiral operators are shown to satisfy polynomial equations over appropriate rings, and the phase structure of the theory can be elegantly described by the factorization of these polynomials into irreducible pieces. In particular, this idea yields a powerful method to analyse the possible smooth interpolations between different classical limits in the gauge theory. As an application in U(N) theories, we provide a simple and completely general proof of the fact that confining and Higgs vacua are in the same phase when fundamental flavors are present, by finding an irreducible polynomial equation satisfied by the glueball operator. We also derive the full phase diagram for the theory with one adjoint when N ≤ 7 using computational algebraic geometry programs.
17016967
The chiral ring and the periods of the resolvent
Abstract The strongly coupled vacua of an N = 1 supersymmetric gauge theory can be described by imposing quantization conditions on the periods of the gauge theory resolvent, or equivalently by imposing factorization conditions on the associated N = 2 Seiberg–Witten curve (the so-called strong-coupling approach). We show that these conditions are equivalent to the existence of certain relations in the chiral ring, which themselves follow from the fact that the gauge group has a finite rank. This provides a conceptually very simple explanation of why and how the strongly coupled physics of N = 1 theories, including fractional instanton effects, chiral symmetry breaking and confinement, can be derived from purely semi-classical calculations involving instantons only.
17626338
Spectral asymmetry and supersymmetry
Fractional charges, and in particular the spectral asymmetry eta of certain Dirac operators, can appear in the central charge of supersymmetric field theories. This yields unexpected analyticity constraints on eta from which classic results can be recovered in an elegant way. The method could also be applied in the context of string theory.
14085932
A Note on theta dependence
Abstract The dependence on the topological θ angle term in quantum field theory is usually discussed in the context of instanton calculus. There the observables are 2 π periodic, analytic functions of θ . However, in strongly coupled theories, the semi-classical instanton approximation can break down due to infrared divergences. Instances are indeed known where analyticity in θ can be lost, while the 2 π periodicity is preserved. In this short Letter we exhibit a simple two-dimensional example where the 2 π periodicity is lost. The observables remain periodic under the transformation θ ↦ θ +2 kπ for some k ⩾2. We also briefly discuss the case of four-dimensional N =2 supersymmetric gauge theories.