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.
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.
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.
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.
14411174
Consistency conditions in the chiral ring of super-Yang Mills theories
Abstract Starting from the generalized Konishi anomaly equations at the non-perturbative level, we demonstrate that the algebraic consistency of the quantum chiral ring of the N = 1 super-Yang–Mills theory with gauge group U ( N ) , one adjoint chiral superfield X and N f ⩽ 2 N flavours of quarks implies that the periods of the meromorphic one-form Tr d z z − X must be quantized. This shows in particular that identities in the open string description of the theory, that follow from the fact that gauge invariant observables are expressed in terms of gauge variant building blocks, are mapped onto non-trivial dynamical equations in the closed string description.
17019473
Nonperturbative double scaling limits
Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path)-integrals by gauge theory or nonlinear σ model (path)-integrals. We explain how this solves one of the most fundamental limitations of the classic approach: we automatically obtain nonperturbative definitions in non-Borel summable cases. This is exemplified in the simplest possible examples involving O(N) symmetric nonlinear σ models with N-dimensional target spaces, for which we construct (multi)critical metrics. The nonperturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path)-integrals.
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.
124943654
FIELD THEORIES AND THE PROBLEM OF TOPOLOGICAL ENTANGLEMENT IN POLYMER PHYSICS
119179081
On a singular Fredholm-type integral equation arising in N=2 super-Yang–Mills theories
Abstract In this work we study the Nekrasov–Shatashvili limit of the Nekrasov instanton partition function of Yang–Mills field theories with N = 2 supersymmetry and gauge group SU ( N c ) . The theories are coupled with N f flavors of fundamental matter. The equation that determines the density of eigenvalues at the leading order in the saddle-point approximation is exactly solved when N f = 2 N c . The dominating contribution to the instanton free energy is computed. The requirement that this energy is finite imposes quantization conditions on the parameters of the theory that are in agreement with analogous conditions that have been derived in previous works. The instanton energy and thus the instanton contribution to the prepotential of the gauge theory is computed in closed form.
119262081
Ring polymers with topological constraints
In the first part of this work a summary is provided of some recent experiments and theoretical results which are relevant in the research of systems of polymer rings in nontrivial topological conformations. Next, some advances in modeling the behavior of single polymer knots are presented. The numerical simulations are performed with the help of the Wang-Landau Monte Carlo algorithm. To sample the polymer conformation a set of random transformations called pivot moves is used. The crucial problem of preserving the topology of the knots after each move is tackled with the help of two new techniques which are briefly explained. As an application, the results of an investigation of the effects of topology on the thermal properties of polymer knots is reported. In the end, original results are discussed concerning the use of parallelized codes to study polymers knots composed by a large number of segments within the Wang-Landau approach.
118880148
A Topological Field Theory for the triple Milnor linking coefficient
The subject of this work is a three-dimensional topological field theory with a non-semisimple group of gauge symmetry with observables consisting in the holonomies of connections around three closed loops. The connections are a linear combination of gauge potentials with coefficients containing a set of one-dimensional scalar fields. It is checked that these observables are both metric independent and gauge invariant. The gauge invariance is achieved by requiring non-trivial gauge transformations in the scalar field sector. This topological field theory is solvable and has only a relevant amplitude which has been computed exactly. From this amplitude it is possible to isolate a topological invariant which is Milnor's triple linking invariant. The topological invariant obtained in this way is in the form of a sum of multiple contour integrals. The contours coincide with the trajectories of the three loops mentioned before. The introduction of the one-dimensional scalar field is necessary in order to reproduce correctly the particular path ordering of the integration over the contours which is present in the triple Milnor linking coefficient. This is the first example of a local topological gauge field theory that is solvable and can be associated to a topological invariant of the complexity of the triple Milnor linking coefficient.