arXiv subjects

N. Dorey

Publications and source records attributed to N. Dorey.

27 records · Page 2Linked to original sources

arXiv1996

Multi-Instanton Check of the Relation Between the Prepotential F and the Modulus u in N=2 SUSY Yang-Mills Theory

By examining multi-instantons in N=2 supersymmetric SU(2) gauge theory, we derive, on very general grounds, and to all orders in the instanton number, a relationship between the prepotential F(Phi), and the coordinate on the quantum moduli space u= . This relation was previously obtained by Matone in the context of the explicit Seiberg-Witten low-energy solution of the model. Our findings can be viewed as a multi-instanton check of the proposed exact results in supersymmetric gauge theory.

hep-th↗

arXiv1996

Multi-Instanton Calculus in $N=2$ Supersymmetric Gauge Theory

The Seiberg-Witten solution of N=2 supersymmetric SU(2) gauge theory may be viewed as a prediction for the infinite family of constants F_n measuring the n-instanton contribution to the prepotential F. Here we examine the instanton physics directly, in particular the contribution of the general self-dual solution of topological charge n constructed by Atiyah, Drinfeld, Hitchin and Manin (ADHM). In both the bosonic and supersymmetric cases, we determine both the large- and short-distance behavior of all the fields in this background. This allows us to construct the exact classical interaction between n ADHM (super-)instantons mediated by the adjoint Higgs. We calculate the one- and two-instanton contributions to the low-energy Seiberg-Witten effective action, and find precise agreement with their predicted values of F_1 and F_2.

hep-th↗

arXiv1996

S-duality in N=4 supersymmetric gauge theories

The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle $θ$. This extended S-duality conjecture includes the case when the unbroken gauge group is non-abelian and a definite prediction for the spectrum of dyons results.

hep-th↗

arXiv1996

Non-abelian duality in N=4 supersymmetric gauge theories

A semi-classical check of the Goddard-Nuyts-Olive (GNO) generalized duality conjecture for gauge theories with adjoint Higgs fields is performed for the case where the unbroken gauge group is non-abelian. The monopole solutions of the theory transform under the non-abelian part of the unbroken global symmetry and the associated component of the moduli space is a Lie group coset space. The well-known problems in introducing collective coordinates for these degrees-of-freedom are solved by considering suitable multi-monopole configurations in which the long-range non-abelian fields cancel. In the context of an $N=4$ supersymmetric gauge theory, the multiplicity of BPS saturated states is given by the number of ground-states of a supersymmetric quantum mechanics on the compact internal moduli space. The resulting degeneracy is expressed as the Euler character of the coset space. In all cases the number of states is consistent with the dimensions of the multiplets of the unbroken dual gauge group, and hence the results provide strong support for the GNO conjecture.

hep-th↗

arXiv1995

Thin Absolute Villains

We perform simulations of an absolute value version of the Villain model on phi3 and phi4 Feynman diagrams, ``thin'' 3-regular and 4-regular random graphs. The phi4 results are in excellent quantitative agreement with the exact calculations by Dorey and Kurzepa for an annealed ensemble of thin graphs, in spite of simulating only a single graph of each size. We also derive exact results for an annealed ensemble of phi3 graphs and again find excellent agreement with the numerical data for single phi3 graphs. The simulations confirm the picture of a mean field vortex transition which is suggested by the analytical results. Further simulations on phi5 and phi6 graphs and of the standard XY model on phi3 graphs confirm the universality of these results. The calculations of Dorey and Kurzepa were based on reinterpreting the large orders behaviour of the anharmonic oscillator in a statistical mechanical context so we also discuss briefly the interpretation of singularities in the large orders behaviour in other models as phase transitions.

hep-lat↗

arXiv1995

Chiral Divergent Properties of Hadrons in the Large-N_c Limit

We compute the leading non-analytic correction to the baryon mass in the combined limits m_π-> 0, N_c -> \infty with the product m_πx N_c held fixed. We reproduce the results of Cohen and Broniowski using semiclassical methods rather than heavy-baryon chiral perturbation theory. The calculation is organized to demonstrate: (1) the model independence of our results; and (2) the crucial role played by (iso)rotations of the hedgehog pion cloud surrounding the baryon. Our rotationally improved large-N_c calculation yields results that naturally interpolate between ordinary chiral perturbation theory on the one hand, and large-N_c physics on the other.

hep-ph↗

arXiv1994

Solvability, Consistency and the Renormalization Group in Large-$N_c$ Models of Hadrons

We establish the following fundamentals about Lagrangian models of meson-baryon interactions in the large-$N_{c}$ limit: 1. Calculating the leading-order contribution to $1$-meson/$2$-baryon Green's functions in the $1/N_c$ expansion involves summing an infinite class of divergent Feynman diagrams. So long as the bare Lagrangian properly obeys all large-$N_c$ selection rules, this all-loops resummation is accomplished exactly by solving coupled classical field equations with a short-distance cutoff. 2. The only effect of the resummation is to renormalize the bare Yukawa couplings, baryon masses and hyperfine baryon mass splittings of the model. 3. In the process, the large-$N_{c}$ renormalization group flow of these bare parameters is completely determined. We conjecture that variants of the Skyrme model emerge as UV fixed points of such flows.

hep-ph↗

arXiv1992

Phase Structure of QED3 at Finite Temperature

Dynamical symmetry breaking in three-dimensional QED with N fermion flavours is considered at finite temperature, in the large $N$ approximation. Using an approximate treatment of the Schwinger-Dyson equation for the fermion self-energy, we find that chiral symmetry is restored above a certain critical temperature which depends itself on $N$. We find that the ratio of the zero-momentum zero-temperature fermion mass to the critical temperature has a large value compared with four-fermion theories, as had been suggested in a previous work with a momentum-independent self-energy. Evidence of a temperature- dependent critical $N$ is shown to appear in this approximation. The phase diagram for spontaneous mass generation in the theory is presented in $T-N$ space.

hep-ph↗

arXiv1992

Vortex condensation in a model of random $ϕ^{4}$-graphs

We consider a soluble model of large $ϕ^{4}$-graphs randomly embedded in one compactified dimension; namely the large-order behaviour of finite-temperature perturbation theory for the partition function of the anharmonic oscillator. We solve the model using semi-classical methods and demonstrate the existence of a critical temperature at which the system undergoes a second-order phase transition from $D=1$ to $D=0$ behaviour. Non-trivial windings of the closed loops in a graph around the compactified time direction are interpreted as vortices. The critical point has a natural interpretation as the temperature at which these vortices condense and disorder the system. We show that the vortex density increases rapidly in the critical region indicating the breakdown of the dilute vortex gas approximation at this point. We discuss the relation of this phenomenon to the Berezinskii-Kosterlitz-Thouless transition in the $D=1$ matrix model formulated on a circle.

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