8282670
Monte Carlo Computation of the Vassiliev knot invariant of degree 2 in the integral representation
In mathematics there is a wide class of knot invariants that may be expressed in the form of multiple line integrals computed along the trajectory C describing the spatial conformation of the knot. In this work it is addressed the problem of evaluating invariants of this kind in the case in which the knot is discrete, i. e. its trajectory is constructed by joining together a set of segments of constant length. Such discrete knots appear almost everywhere in numerical simulations of systems containing one dimensional ring-shaped objects. Examples are polymers, the vortex lines in fluids and superfluids like helium and other quantum liquids. Formally, the trajectory of a discrete knot is a piecewise smooth curve characterized by sharp corners at the joints between contiguous segments. The presence of these corners spoils the topological invariance of the knot invariants considered here and prevents the correct evaluation of their values. To solve this problem, a smoothing procedure is presented, which eliminates the sharp corners and transforms the original path C into a curve that is everywhere differentiable. The procedure is quite general and can be applied to any discrete knot defined off or on lattice. This smoothing algorithm is applied to the computation of the Vassiliev knot invariant of degree 2 denoted here with the symbol (C). This is the simplest knot invariant that admits a definition in terms of multiple line integrals. For a fast derivation of (C), it is used a Monte Carlo integration technique. It is shown that, after the smoothing, the values of (C) may be evaluated with an arbitrary precision. Several algorithms for the fast computation of the Vassiliev knot invariant of degree 2 are provided.
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.
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.
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.
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.
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.
119253138
2D Quantum Gravity at One Loop with Liouville and Mabuchi Actions
Abstract We study a new two-dimensional quantum gravity theory, based on a gravitational action containing both the familiar Liouville term and the Mabuchi functional, which has been shown to be related to the coupling of non-conformal matter to gravity. We compute the one-loop string susceptibility from a first-principle, path integral approach in the Kahler parameterization of the metrics and discuss the particularities that arise in the case of the pure Mabuchi theory. While we mainly use the most convenient spectral cutoff regularization to perform our calculations, we also discuss the interesting subtleties associated with the multiplicative anomaly in the familiar ζ -function scheme, which turns out to have a genuine physical effect for our calculations. In particular, we derive and use a general multiplicative anomaly formula for Laplace-type operators on arbitrary compact Riemann surfaces.
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.
15879418
The proof of the Dijkgraaf-Vafa conjecture and application to the mass gap and confinement problems.
Using generalized Konishi anomaly equations, it is known that one can express, in a large class of supersymmetric gauge theories, all the chiral operators expectation values in terms of a finite number of a priori arbitrary constants. We show that these constants are fully determined by the requirement of gauge invariance and an additional anomaly equation. The constraints so obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa quantum glueball superpotential, with all terms (including the Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill non-trivial gaps in existing derivations of the mass gap and confinement properties in super Yang-Mills 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.