119961620
NONSTANDARD CONFORMAL FIELD THEORIES FROM THE b-c SYSTEMS ON GENERAL ALGEBRAIC CURVES
In this paper we develop an operator formalism for the b–c systems with conformalweight λ=1 defined on a general closed and orientable Riemann surface. The advantageof our approach is that the Riemann surface is represented as an affine algebraic curve.In this way it is possible to show that the b–c systems at higher genera are equivalentto nonstandard conformal field theories on the complex sphere. The amplitudes of theseconformal field theories, rigorously computed using simple normal ordering prescriptions,are single-valued on the algebraic curve and coincide with the correlation functions of theoriginal b–c systems. Besides the obvious applications in string theories and conformalfield theories, (the b–c systems at λ=1 are intimately related to the free scalar fieldtheory), the operator formalism presented here also sheds some light on the quantizationof field theories on Riemann surfaces.
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.
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.
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.
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.
119318242
Partial Gauge Fixing and Equivariant Cohomology
Given a gauge theory with gauge group G, it is sometimes useful to find an equivalent formulation in terms of a nontrivial gauge subgroup H⊂G. This amounts to fixing the gauge partially from G down to H. We study this problem systematically, both from the algebraic and from the path integral points of view. We find that the usual BRST cohomology must be replaced by an equivariant version and that the ghost Lagrangian must always include quartic ghost terms, even at tree level. Both the Cartan and Weil models for equivariant cohomology play a role and find natural interpretations within the physics framework. Applications include the construction of D-brane models of emergent space, the 't Hooft Abelian projection scenario in quantum chromodynamics and the formulation of the low-energy effective theories of grand unified models. © 2014 American Physical Society.
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.
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.
119574064
Multi-loop zeta function regularization and spectral cutoff in curved spacetime
Abstract We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard zeta function regularization at one loop and, on the other hand, a natural generalization of this method to higher loops. In particular, to any Feynman diagram is associated a generalized meromorphic zeta function. For the one-loop vacuum diagram, it is directly related to the usual spectral zeta function. To any loop order, the renormalized amplitudes can be read off from the pole structure of the generalized zeta functions. We focus on scalar field theories and illustrate the general formalism by explicit calculations at one-loop and two-loop orders, including a two-loop evaluation of the conformal anomaly.