119806289
O(N) Generalized nonlinear sigma model and its applications
In this work the results of an interdisciplinary research between field theory and statistical mechanics will be presented. It is shown that the dynamics of an inextensible chain is described by a slight generalization of the O(d) nonlinear sigma model. It is checked, that in the large time limit the correct equilibrium distribution is reached. Our approach is based on path integrals, but it may be also connected to the usual description of the dynamics of a chain as a diffusion stochastic process. Some applications of our results will be discussed, like for instance the calculation of the average distance between two polymer segments.
116932271
Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain
Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant.
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.
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.
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.
117767120
Operator formalism for b-c systems with lambda = 1 on general algebraic curves
In this letter we develope an operator formalism for the $b-c$ systems with conformal weight $\lambda=1$ defined on a general closed and orientable Riemann surface. The advantage of our approach is that the Riemann surface is represented as an affine algebraic curve. In this way it is possible to perform explicit calculations in string theory at any perturbative order. Besides the obvious applications in string theories and conformal field theories, (the $b-c$ systems at $\lambda=1$ are intimately related to the free scalar field theory), the operator formalism presented here sheds some light also on the quantization of field theories on Riemann surfaces. In fact, we are able to construct explicitly the vacuum state of the $b-c$ systems and to define creation and annihilation operators. All the amplitudes are rigorously computed using simple normal ordering prescriptions as in the flat case.
14626342
Exact amplitudes in four-dimensional non-critical string theories
Abstract The large N expansion of N =2 supersymmetric Yang–Mills theory with gauge group SU( N ) has recently been shown to break down at singularities on the moduli space. We conjecture that by taking N →∞ and approaching the singularities in a correlated way, all the observables of the theory have a finite universal limit yielding amplitudes in string theories dual to field theories describing the light degrees of freedom. We explicitly calculate the amplitudes corresponding to the Seiberg–Witten period integrals for an A n −1 series of multicritical points as well as for other critical points exhibiting a scaling reminiscent of the c =1 matrix model. Our results extend the matrix model approach to non-critical strings in less than one dimension to non-critical strings in four dimensions.
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.
16567547
Exact multiplets of spontaneously broken discrete global symmetries: The example of N=2 SUSY QCD
In these notes, we emphasize the r\^ole of spontaneous broken global discrete symmetries acting on the moduli space of $N=2$ susy Yang-Mills theories and show how they can be used, together with the BPS condition, as a spectrum generating symmetry. In particular, in the strong-coupling region, all BPS states come in multiplets of this broken symmetry. This played a key r\^ole in the determination of the strong-coupling spectra.
17019473
Nonperturbative double scaling limits
Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path)-integrals by gauge theory or nonlinear σ model (path)-integrals. We explain how this solves one of the most fundamental limitations of the classic approach: we automatically obtain nonperturbative definitions in non-Borel summable cases. This is exemplified in the simplest possible examples involving O(N) symmetric nonlinear σ models with N-dimensional target spaces, for which we construct (multi)critical metrics. The nonperturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path)-integrals.
15406996
Microscopic quantum superpotential in = 1 gauge theories
We consider the = 1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential Wmic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, Wmic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of = 2 super Yang-Mills theories to the realm of = 1 gauge theories.