119193278
Dynamical aspects of inextensible chains
In the present work the dynamics of a continuous inextensible chain is studied. The chain is regarded as a system of small particles subjected to constraints on their reciprocal distances. It is proposed a treatment of systems of this kind based on a set Langevin equations in which the noise is characterized by a non-gaussian probability distribution. The method is explained in the case of a freely hinged chain. In particular, the generating functional of the correlation functions of the relevant degrees of freedom which describe the conformations of this chain is derived. It is shown that in the continuous limit this generating functional coincides with a model of an inextensible chain previously discussed by one of the authors of this work. Next, the approach developed here is applied to a inextensible chain, called the freely jointed bar chain, in which the basic units are small extended objects. The generating functional of the freely jointed bar chain is constructed. It is shown that it differs profoundly from that of the freely hinged chain. Despite the differences, it is verified that in the continuous limit both generating functionals coincide as it is expected.
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.
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.
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.
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.
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.
119308173
Simple matrix models for random Bergman metrics
Recently, the authors have proposed a new approach to the theory of random metrics, making an explicit link between probability measures on the space of metrics on a Kahler manifold and random matrix models. We consider simple examples of such models and study the one- and two-point functions of the metric. These geometric correlation functions correspond to new interesting types of matrix model correlators. We provide in particular a detailed study of the Wishart model, where we determine the correlation functions explicitly. We find that the random measure in this model turns out to be concentrated on the background metric in the large N limit.
37616
Glueball operators and the microscopic approach to N = 1 gauge theories
We explain how to generalize Nekrasov's microscopic approach to = 2 gauge theories to the = 1 case, focusing on the typical example of the U(N) theory with one adjoint chiral multiplet X and an arbitrary polynomial tree-level superpotential Tr W(X). We provide a detailed analysis of the generalized glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa matrix model and of the generalized Konishi anomaly equations. We compute in particular the non-trivial quantum corrections to the Virasoro operators and algebra that generate these equations. We have performed explicit calculations up to two instantons, that involve the next-to-leading order corrections in Nekrasov's Ω-background.
16340483
The strong coupling spectrum of the Seiberg-Witten theory
Abstract We carefully study the global structure of the solution of the N = 2 supersymmetric pure Yang-Mills theory with gauge group SU(2) obtained by Seiberg and Witten. We exploit itsZsymmetry and describe the curve in moduli space where BPS states can become unstable, separating the strong-coupling from the weak-coupling region. This allows us to obtain the spectrum of stable BPS states in the strong-coupling region: we prove that only the two particles responsible for the singularities of the solution (the magnetic monopole and the dyon of unit electric charge) are present in this region. Our method also permits us to very easily obtain the weak-coupling spectrum, without using semiclassical methods. We discuss how the BPS states disintegrate when crossing the border from the weak- to the strong-coupling region.
118493409
D-Brane Probes in the Matrix Model
Abstract Recently, a new approach to large N gauge theories, based on a generalization of the concept of D-brane probes to any gauge field theory, was proposed. In the present note, we compute the probe action in the one matrix model with a quartic potential. This allows to illustrate several non-trivial aspects of the construction in an exactly solvable set-up. One of our main goal is to test the bare bubble approximation. The approximate free energy found in this approximation, which can be derived from a back-of-an-envelope calculation, matches the exact result for all values of the 't Hooft coupling with a surprising accuracy. Another goal is to illustrate the remarkable properties of the equivariant partial gauge-fixing procedure, which is at the heart of the formalism. For this we use a general ξ -gauge to compute the brane action. The action depends on ξ in a very non-trivial way, yet we show explicitly that its critical value does not and coincides with twice the free energy, as required by general consistency. This is made possible by a phenomenon of ghost condensation and the spontaneous breaking of the equivariant BRST symmetry.