17441439
Flavors in the microscopic approach to = 1 gauge theories
In this note, we solve an extended version of the = 1 super Yang-Mills theory with gauge group U(N), an adjoint chiral multiplet and Nf flavors of quarks, by using the = 1 microscopic formalism based on Nekrasov's sums over colored partitions. Our main new result is the computation of the general mesonic operators. We prove that the generalized Konishi anomaly equations with flavors are satisfied at the non-perturbative level. This yields in particular a microscopic, first principle derivation of the matrix model disk diagram contributions that must be included in the Dijkgraaf-Vafa approach.
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.
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.
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.
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.
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.
62788967
On a possible approach to general field theories with nonpolynomial interactions
In this work a class of massive scalar field theories with self-interactions described by a general potential is studied. Under the sole condition that the potential admits the Fourier representation, it is shown that such theories may be mapped into a standard field theory, in which the interaction of the new fields is a polynomial of fourth degree. With some restrictions, this mapping allows the perturbative treatment of models that are otherwise intractable with standard field theoretical methods. 
A nonperturbative approach to these theories is attempted. The original scalar field is integrated out exactly at the price of introducing auxiliary vector fields. The latter are treated in a mean field theory approximation. The singularities that arise after the elimination of the auxiliary fields are cured using the dimensional regularization. The expression of the counterterms to be subtracted is computed.
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.
51824208
Topological entanglement of polymers and Chern-Simons field theory
In recent times some interesting field-theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static polymers or in a lattice of obstacles is considered. The extension to the case in which the configurations of two or more polymers become non-static is not straightforward unless their trajectories are severely constrained. In this paper we present another approach, based on Chern-Simons field theory, which is able to describe the topological entanglements of two fluctuating polymers in terms of gauge fields and second quantized replica fields.
123165628
ON THE PARTITION FUNCTION OF STRING THEORIES DEFINED ON ALGEBRAIC CURVES
In this paper the amplitudes of bosonic string theory on Riemann surfaces are studied taking the branch points as moduli. The case of a general Riemann surface of genus three is completely worked out, constructing the chiral determinants and the propagators. The chiral determinants and the partition function are given explicitly in terms of the moduli and of the parameters of the curve apart from a factor which is essentially a theta constant. The Beilinson-Manin formulae for Riemann surfaces whose moduli space is parametrized by branch points are discussed.
16793358
FIELD THEORIES ON THE POINCARÉ DISK
The massive scalar field theory and the chiral Schwinger model are quantized on a Poincare disk of radius ρ. The amplitudes are derived in terms of Legendre functions. The behavior at long distances and near the boundary of some of the relevant correlation functions is studied. The exact computation of the chiral determinant appearing in the Schwinger model is obtained exploiting perturbation theory. This calculation poses interesting mathematical problems, as the Poincare disk is a noncompact manifold with a metric tensor which diverges when it approaches the boundary. The results presented in this paper are very useful in view of possible extensions to general Riemann surfaces. Moreover, they could also shed some light in the quantization of field theories on manifolds with constant curvature scalars in higher dimensions.