209869150
The microscopic approach to N=1 super Yang-Mills theories
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.
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.
15472365
Quantum parameter space and double scaling limits in N=1 super Yang-Mills theory
We study the physics of $\mathcal{N}=1$ super Yang-Mills theory with the gauge group $\mathrm{U}(N)$ and one adjoint Higgs field, by using the recently derived exact effective superpotentials. Interesting phenomena occur for some special values of the Higgs potential couplings. We find critical points with massless glueballs and/or massless monopoles, confinement without a mass gap, and tensionless domain walls. We describe the transitions between regimes with different patterns of gauge symmetry breaking, or, in the matrix model language, between solutions with a different number of cuts. The standard large N expansion is singular near the critical points, with domain wall tensions scaling as a fractional power of N. We argue that the critical points are four-dimensional analogues of the Kazakov critical points that are commonly found in low dimensional matrix integrals. We define a double scaling limit that yields the exact tension of BPS two-branes in the resulting $\mathcal{N}=1,$ four-dimensional noncritical string theory. D-brane states can be deformed continuously into closed string solitonic states, and vice versa, along paths that go over regions where the string coupling is strong.
1817006
Curves of marginal stability, and weak- and strong-coupling BPS spectra in N = 2 supersymmetric QCD
We explicitly determine the global structure of the SL(2, Z) bundle over the Coulomb branch of the moduli space of asymptotically free N = 2 supersymmetric Yang-Mills theories with gauge group SU(2) when massless hypermultiplets are present. For each relevant number of flavours, we show that there is a curve of marginal stability of the Coulomb branch, diffeomorphic to a circle, across which the BPS spectrum is discontinuous. We determine rigorously and completely the BPS spectra inside and outside the curve. In all cases, the spectrum inside the curve consists of only those BPS states that are responsible for the singularities of the low energy effective action (in addition to the massless abelian gauge multiplet which is always present). The predicted decay patterns across the curve of marginal stability are perfectly consistent with all quantum numbers carried by the BPS states. As a byproduct, we also show that the electric and magnetic quantum numbers of the massless states at the singularities proposed by Seiberg and Witten are the only possible ones.
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.
123697695
STRING THEORIES ON RIEMANN SURFACES OF ALGEBRAIC FUNCTIONS
In this paper we extend to a general Riemann surface a formalism used so far for surfaces with Abelian group of symmetry. Using an algebraic equation F(z, w)=0 to define the surface in terms of sheets and branch points, it is possible to construct the correlation functions for b—c systems with integer conformal weight j and for the scalar fields X. Explicit examples are provided for a general surface of genus three and a surface of genus four. No essential complication arises with respect to the hyperelliptic case. At the end we discuss the computation of chiral determinants det using the stress energy tensor method.
124943654
FIELD THEORIES AND THE PROBLEM OF TOPOLOGICAL ENTANGLEMENT IN POLYMER PHYSICS
118089538
Gauge Field Theories on Riemann Surfaces
In this paper the free gauge field theories on a Riemann surface of any genus are quantized in the covariant gauge. The propagators of the gauge fields are explicitly derived and their properties are analysed in details. As an application, the correlation functions of a Yang-Mills field theory with gauge group $SU(N)$ are computed at the lowest order.
12681174
Operator formalism for bosonic beta gamma fields on general algebraic curves
An operator formalism for bosonic β–γ system on arbitrary algebraic curves is introduced. The classical degrees of freedom are identified and their commutation relations are postulated. The explicit realization of the algebra formed by the fields is given in the Hilbert space equipped with a bilinear form. The construction is based on the “Gaussian” representation for β–γ system on the complex sphere [Alvarez-Gaume et al., Nucl. Phys. B 311, 333 (1988)]. Detailed computations are provided for two- and four-point correlation functions.
119268708
On a field theoretical model of polymeric $2s-$plats and some of its consequences
The main subject of this work is the statistical mechanics of a system of N polymer rings linked together. The link that arises in this way is constrained to be in the form of a 2s-plat, where 2s is the fixed number of maxima and minima of the polymer trajectories along one chosen direction. Plats appear very often in nature, in particular in the DNA of living organisms. The topological states of the link are distinguished using the Gauss linking number. This is a relatively weak link invariant in the case of a general link, but its efficiency improves when 2s-plats are considered as it will be proved here. Using field theoretical methods, a nonperturbative expression of the partition function of the system is achieved. In its final form, this partition function is equivalent to that of a multi-layer electron gas. Such quasi-particle systems are studied in connection with several interesting applications, including high-Tc superconductivity and topological quantum computing. It is shown that the topological constraints acting on the polymer rings generate two and three-body forces acting on the monomers. These forces interphere with the non-topological two-body forces to which monomers are subjected in a solution, enhancing for instance the attraction between the monomers. What is remarkable is the appearance of three-body forces of topological origin. It is shown that these three-body interactions have nonvanishing contributions when three or more rings are entangled together.