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.
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.
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.
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.
14323623
Chern-Simons field theories in the Coulomb gauge
An integrated precision reference source for supplying a reference voltage or a reference current under the condition of a lower feed voltage is disclosed, includes a first transistor, a first resistor connected between base and collector of the first transistor, a second resistor connected between base and emitter of the first transistor, and a second transistor whose base is connected to the collector of the first transistor and whose emitter is connected through a third resistor to the emitter of the first transistor.
15099856
Topologically nontrivial sectors of the Maxwell field theory on algebraic curves
Abstract In this paper a large family of nondegenerate metrics is derived on general algebraic curves. In this way, it is possible to treat many differential equations arising in quantum mechanics and field theories on Riemann surfaces as differential equations on the complex sphere. The case of the Maxwell field theories on curves with Z n group of automorphisms is studied in details. These curves are particularly important because they cover the entire moduli space spanned by the Riemann surfaces of genus g ≤ 2. All the classical solutions of the Maxwell equations are explicitly constructed. Also the examples of the scalar fields and of an electron immersed in a constant magnetic field will be briefly investigated.
116932271
Applications of a generalization of the nonlinear sigma model with O(d) group of symmetry to the dynamics of a constrained chain
Subject of this work are the applications of a field theoretical model, called here generalized nonlinear sigma model or simply GNLSM,to the dynamics of a chain subjected to constraints. Chains with similar properties and constraints have been discussed in a seminal paper of Edwards and Goodyear using an approach based on the Langevin equation. The GNLSM has been proposed in a previous publication in order to describe the dynamics of a two dimensional chain. In this paper the model is extended to d dimensions and a bending energy term is added to its action. As an application, two observables are computed in the case of a very stiff chain. The first observable is the dynamical form factor of a ring shaped chain. The second observable is a straightforward generalization to dynamics of the static form factor. This observable is relevant in order to estimate the average distance between two arbitrary points of the chain. Finally, a variant of the GNLNM is presented, in which the topological conditions which constrain the motion of two linked chains are imposed with the help of the Gauss linking invariant.
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.
13162040
On the Quantization of Abelian Gauge Field Theories on Riemann Surfaces
In this paper general abelian gauge field theories interacting with matter fields are quantized on a closed and orientable Riemann surface $\Sigma$. The approach used is that of small perturbations around topologically nontrivial classical solutions $A^I_\mu$ of the Maxwell equations. The propagator of the gauge fields and the form of the fields $A^I_\mu$ are explicitly computed in the Feynman gauge. Despite of the fact that the quantization procedure presented here is mainly perturbative, in the case of the Schwinger model, or two dimensional quantum electrodynamics, it is also possible to derive nonperturbative results. As an example, we show that, at very short distances, the electromagnetic forces on a Riemann surface vanish up to zero modes.