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.
13918426
On the Quantization of the Chern-Simons Fields Theory on Curved Space-Times: the Coulomb Gauge Approach
We consider here the Chern-Simons field theory with gauge group SU(N) in the presence of a gravitational background that describes a two-dimensional expanding “universe”. Two special cases are treated here in detail: the spatially flat Robertson-Walker space-time and the conformally static space-times having a general closed and orientable Riemann surface as spatial section. The propagator and the vertices are explicitely computed at the lowest order in perturbation theory imposing the Coulomb gauge fixing. March 1993 1 Work supported by the Consiglio Nazionale Ricerche, P.le A. Moro 7, Roma, Italy
118564185
Dynamics of two topologically entangled chains
Starting from a given topological invariant, we argue that it is possible to construct a topological field theory with a finite number of Feynman diagrams and an amplitude of gauge invariant objects that is a function of that invariant. This is, for example, the case of the Gauss linking number and of the abelian BF models which have been already successfully applied in the statistical mechanics of polymers. In this work it is shown that a suitable generalization of the BF model can be applied also to polymer dynamics, where the polymer trajectories are not static, but change their shape during time.
14104352
The neurochip Totem : a case study in HEP
It is being proved that the neurochip Totem is a viable solution for high quality and real time computational tasks in HEP, including event classification, triggering and signal processing. The architecture of the chip is based on a ”derivative free” algorithm called Reactive Tabu Search (RTS), highly performing even for low precision weights. ISA, VME or PCI boards integrate the chip as a coprocessor in a host computer. This paper presents: 1) the state of the art and the next evolution of the design of Totem; 2) its ability in the Higgs search at LHC as an example. Reference number: 303
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.
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.
119685691
Gravitational actions in two dimensions and the Mabuchi functional
Abstract The Mabuchi energy is an interesting geometric functional on the space of Kahler metrics that plays a crucial role in the study of the geometry of Kahler manifolds. We show that this functional, as well as other related geometric actions, contribute to the effective gravitational action when a massive scalar field is coupled to gravity in two dimensions in a small mass expansion. This yields new theories of two-dimensional quantum gravity generalizing the standard Liouville models.
15870966
Large N and double scaling limits in two dimensions
Recently, the author has constructed a series of four dimensional non-critical string theories with eight supercharges, dual to theories of light electric and magnetic charges, for which exact formulas for the central charge of the space-time supersymmetry algebra as a function of the world-sheet couplings were obtained. The basic idea was to generalize the old matrix model approach, replacing the simple matrix integrals by the four dimensional matrix path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov critical points by the Argyres-Douglas critical points. In the present paper, we study qualitatively similar toy path integrals corresponding to the two dimensional N=2 supersymmetric non-linear sigma model with target space CP^n and twisted mass terms. This theory has some very strong similarities with N=2 super Yang-Mills, including the presence of critical points in the vicinity of which the large n expansion is IR divergent. The model being exactly solvable at large n, we can study non-BPS observables and give full proofs that double scaling limits exist and correspond to universal continuum limits. A complete characterization of the double scaled theories is given. We find evidence for dimensional transmutation of the string coupling in some non-critical string theories. We also identify en passant some non-BPS particles that become massless at the singularities in addition to the usual BPS states.
31469664
FQHE on curved backgrounds, free fields and large N
A bstractWe study the free energy of the Laughlin state on curved backgrounds, starting from the free field representation. A simple argument, based on the computation of the gravitational effective action from the transformation properties of Green functions under the change of the metric, allows to compute the first three terms of the expansion in large magnetic field. The leading and subleading contributions are given by the Aubin-Yau and Mabuchi functionals respectively, whereas the Liouville action appears at next-to-next-to-leading order. We also derive a path integral representation for the remainder terms. They correspond to a large mass expansion for a related interacting scalar field theory and are thus given by local polynomials in curvature invariants.
119513982
Super Yang-Mills, matrix models and geometric transitions
Super Yang-Mills, modeles de matrices et transitions geometriques. J'expose deux applications de la relation entre les theories de jauge supersymetriques N = 1 a quatre dimensions, les modeles de matrices jauges a zero dimension, et les transitions geometriques en theorie des cordes. La premiere traite du spectre des parois ou branes BPS. Il est demontre qu'un etat de type D-brane, dont la tension en couplage faible est proportionnelle a N ∼ 1/g s , et un etat de type soliton de corde fermee, dont la tension en couplage faible est proportionnelle a N 2 ∼ 1/g 2 s , peuvent etre continument deformes l'un en l'autre. Ceci est un aspect de la theorie plus generale des espaces quantiques de parametres N = 1. La deuxieme est une nouvelle methode, purement geometrique, pour calculer exactement la somme sur les diagrammes planaires en zero dimension. C'est un exemple de dualite entre cordes ouvertes et cordes fermees.
6368521
Planar diagrams and Calabi-Yau spaces
Large N geometric transitions and the Dijkgraaf-Vafa conjecture suggest a deep relationship between the sum over planar diagrams and Calabi-Yau threefolds. We explore this correspondence in details, explaining how to construct the Calabi-Yau for a large class of Mmatrix models, and how the geometry encodes the correlators. We engineer in particular two-matrix theories with potentials W (X; Y ) that reduce to arbitrary functions in the commutative limit. We apply the method to calculate all correlators htr X p i and htr Y p i in models of the form W (X; Y )= V (X )+ U(Y ) XY and W (X; Y )= V (X )+ YU (Y 2 )+ XY 2 . The solution of the latter example was not known, but when U is a constant we are able to solve the loop equations, nding a precise match with the geometric approach. We also discuss special geometry in multi-matrix models, and we derive an important property, the entanglement of eigenvalues, governing the expansion around classical vacua for which the matrices do not commute.