arXiv subjects

N. Dorey

Publications and source records attributed to N. Dorey.

At least 19 recordsLinked to original sources

arXiv2006

Deconstruction of the Maldacena-Nunez Compactification

We demonstrate a classical equivalence between the large-N limit of the Higgsed N=1* SUSY U(N) Yang-Mills theory and the Maldacena-Nunez twisted compactification of a six dimensional gauge theory on a two-sphere. A direct comparison of the actions and spectra of the two theories reveals them to be identical. We also propose a gauge theory limit which should describe the corresponding spherical compactification of Little String Theory.

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arXiv2005

Spherical Deconstruction

We present evidence that N=1* SUSY Yang-Mills provides a deconstruction of a six-dimensional gauge theory compactified on a two-sphere. The six-dimensional theory is a twisted compactification of N=(1,1) SUSY Yang-Mills theory of the type considered by Maldacena and Nunez (MN). In particular, we calculate the full classical spectrum of the N=1* theory with gauge group U(N) in its Higgs vacuum. In the limit N goes to infinity, we find an exact agreement with the Kaluza-Klein spectrum of the MN compactification.

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arXiv1999

Multi-Instanton Calculus and the AdS/CFT Correspondence in N=4 Superconformal Field Theory

We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field- and string-theoretic derivations of the N=4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions G_n, n=16, 8 or 4, in N=4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero modes are saturated. In the large-N limit, for the first time in any 4-dimensional theory, we are able to evaluate all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of a single copy of AdS_5 x S^5. (2) The integration measure on this space includes the partition function of 10-dimensional N=1 SU(k) gauge theory dimensionally reduced to 0 dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instanton level, G_n = \sqrt{N} g^8 k^{n-7/2} e^{2πikτ} \sum_{d|k} d^{-2} F_n(x_1,...,x_n), where F_n is identical to a convolution of n bulk-to-boundary supergravity propagators.

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arXiv1999

An Elliptic Superpotential for Softly Broken N=4 Supersymmetric Yang-Mills Theory

An exact superpotential is derived for the N=1 theories which arise as massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to coincide with the complexified potential of the N-body elliptic Calogero-Moser Hamiltonian. This superpotential reproduces the vacuum structure predicted by Donagi and Witten for the corresponding four-dimensional theory and also transforms covariantly under the S-duality group of N=4 SYM. The analysis yields exact formulae with interesting modular properties for the condensates of gauge-invariant chiral operators in the four-dimensional theory.

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arXiv1999

The BPS Spectra of Gauge Theories in Two and Four Dimensions

We study N=(2,2) supersymmetric abelian gauge theories in two dimensions. The exact BPS spectrum of these models is shown to coincide with the spectrum of massive hypermultiplets of certain N=2 supersymmetric gauge theories in four dimensions. A special case of these results involves a surprising connection between four-dimensional N=2 SQCD with N colours and N_{f}>N flavours at the root of the baryonic Higgs branch and the supersymmetric CP^{2N-N_{f}-1} sigma-model in two dimensions. This correspondence implies a new prediction for the strong-coupling spectrum of the four-dimensional theory.

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arXiv1998

Multi-Instantons and Maldacena's Conjecture

We examine certain n-point functions G_n in {\cal N}=4 supersymmetric SU(N) gauge theory at the conformal point. In the large-N limit, we are able to sum all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of AdS_5 x S^5. (2) In exact agreement with type IIB superstring calculations, at the k-instanton level, $G_n = \sqrt{N} g^8 k^{n-7/2} e^{-8π^2 k/g^2}\sum_{d|k} d^{-2} \times F_n(x_1,...,x_n)$, where F_n is identical to a convolution of n bulk-to-boundary SUGRA propagators.

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arXiv1998

Yang-Mills Instantons in the Large-N Limit and the AdS/CFT Correspondence

We examine a certain 16-fermion correlator in {\cal N}=4 supersymmetric SU(N) gauge theory in 4 dimensions. Generalizing recent SU(2) results of Bianchi, Green, Kovacs and Rossi, we calculate the exact N-dependence of the effective 16-fermion vertex at the 1-instanton level, and find precise agreement in the large-N limit with the prediction of the type IIB superstring on AdS_5 x S^5. This suggests that the string theory prediction for the 1-instanton amplitude considered here is not corrected by higher-order terms in the alpha' expansion.

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arXiv1998

The BPS Spectra of Two-Dimensional Supersymmetric Gauge Theories with Twisted Mass Terms

The vacuum structure and spectra of two-dimensional gauge theories with N=(2,2) supersymmetry are investigated. These theories admit a twisted mass term for charged chiral matter multiplets. In the case of a U(1) gauge theory with N chiral multiplets of equal charge, an exact description of the BPS spectrum is obtained for all values of the twisted masses. The BPS spectrum has two dual descriptions which apply in the Higgs and Coulomb phases of the theory respectively. The two descriptions are related by a massive analog of mirror symmetry: the exact mass formula which is given by a one-loop calculation in the Coulomb phase gives predictions for an infinite series of instanton corrections in the Higgs phase. The theory is shown to exhibit many phenomena which are usually associated with N=2 theories in four dimensions. These include BPS-saturated dyons which carry both topological and Noether charges, non-trivial monodromies of the spectrum in the complex parameter space, curves of marginal stability on which BPS states can decay and strongly coupled vacua with massless solitons and dyons.

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arXiv1998

Instanton Effects in Three-Dimensional Supersymmetric Gauge Theories with Matter

Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that the asymptotic metric on the Coulomb branch coincides with the metric on Dancer's deformation of the monopole moduli space. For the N=2 theory with $N_f$ flavors, we compute the one-loop corrections to the metric and complex structure on the Coulomb branch. We then determine the superpotential including one-loop effects around the instanton background. These calculations provide an explicit check of several results previously obtained by symmetry and holomorphy arguments.

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arXiv1997

Supersymmetry and the Multi-Instanton Measure II: From N=4 to N=0

Extending recent N=1 and N=2 results, we propose an explicit formula for the integration measure on the moduli space of charge-n ADHM multi-instantons in N=4 supersymmetric SU(2) gauge theory. As a consistency check, we derive a renormalization group relation between the N=4, N=2, and N=1 measures. We then use this relation to construct the purely bosonic (``N=0'') measure as well, in the classical approximation in which the one-loop small-fluctuations determinants is not included.

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arXiv1997

Supersymmetry and the Multi-Instanton Measure

We propose explicit formulae for the integration measure on the moduli space of charge-n ADHM multi-instantons in N=1 and N=2 supersymmetric gauge theories. The form of this measure is fixed by its (super)symmetries as well as the physical requirement of clustering in the limit of large spacetime separation between instantons. We test our proposals against known expressions for n < 3. Knowledge of the measure for all n allows us to revisit, and strengthen, earlier N=2 results, chiefly: (1) For any number of flavors N_F, we provide a closed formula for F_n, the n-instanton contribution to the Seiberg-Witten prepotential, as a finite-dimensional collective coordinate integral. This amounts to a solution, in quadratures, of the Seiberg-Witten models, without appeal to electric-magnetic duality. (2) In the conformal case N_F=4, this means reducing to quadratures the previously unknown finite renormalization that relates the microscopic and effective coupling constants, τ_{micro} and τ_{eff}. (3) Similar expressions are given for the 4-derivative/8-fermion term in the gradient expansion of N=2 supersymmetric QCD.

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arXiv1997

Instantons, Higher-Derivative Terms, and Nonrenormalization Theorems in Supersymmetric Gauge Theories

We discuss the contribution of ADHM multi-instantons to the higher-derivative terms in the gradient expansion along the Coulomb branch of N=2 and N=4 supersymmetric SU(2) gauge theories. In particular, using simple scaling arguments, we confirm the Dine-Seiberg nonperturbative nonrenormalization theorems for the 4-derivative/8-fermion term in the two finite theories (N=4, and N=2 with N_F=4).

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arXiv1997

Multi-Instantons, Three-Dimensional Gauge Theory, and the Gauss-Bonnet-Chern Theorem

We calculate multi-instanton effects in a three-dimensional gauge theory with N=8 supersymmetry and gauge group SU(2). The k-instanton contribution to an eight-fermion correlator is found to be proportional to the Gauss-Bonnet-Chern integral of the Gaussian curvature over the centered moduli-space of charge-k BPS monopoles, \tilde{M}_{k}. For k=2 the integral can be evaluated using the explicit metric on \tilde{M}_{2} found by Atiyah and Hitchin. In this case the integral is equal to the Euler character of the manifold. More generally the integral is the volume contribution to the index of the Euler operator on \tilde{M}_{k}, which may differ from the Euler character by a boundary term. We conjecture that the boundary terms vanish and evaluate the multi-instanton contributions using recent results for the cohomology of \tilde{M}_{k}. We comment briefly on the implications of our result for a recently proposed test of M(atrix) theory.

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arXiv1997

Instantons, Three-Dimensional Gauge Theory, and the Atiyah-Hitchin Manifold

We investigate quantum effects on the Coulomb branch of three-dimensional N=4 supersymmetric gauge theory with gauge group SU(2). We calculate perturbative and one-instanton contributions to the Wilsonian effective action using standard weak-coupling methods. Unlike the four-dimensional case, and despite supersymmetry, the contribution of non-zero modes to the instanton measure does not cancel. Our results allow us to fix the weak-coupling boundary conditions for the differential equations which determine the hyper-Kahler metric on the quantum moduli space. We confirm the proposal of Seiberg and Witten that the Coulomb branch is equivalent, as a hyper-Kahler manifold, to the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin.

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arXiv1996

On Mass-Deformed N=4 Supersymmetric Yang-Mills Theory

We construct the n-instanton action for the above model with gauge group SU(2), as a function of the collective coordinates of the general self-dual configurations of Atiyah, Drinfeld, Hitchin and Manin (ADHM). We calculate the quantum modulus u = at the 1-instanton level, and find a discrepancy with Seiberg and Witten's proposed exact solution. As in related models (N=2, N_F=3 or 4), this discrepancy may be resolved by modifying their proposed relation between $\tilde u$ (the parameter in the elliptic curve) and u.

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arXiv1996

On N=2 Supersymmetric QCD with 4 Flavors

Seiberg and Witten's proposed solution of N=2 SQCD with N_c=2 and N_F=4 is known to conflict with instanton calculations in three distinct ways. Here we show how to resolve all three discrepancies, simply by reparametrizing the elliptic curve in terms of quantities $τ^0_{eff}$ and $\tilde{u}$ rather than $τ$ and $u = < Tr A^2 > $. SL(2,Z) invariance of the curve is preserved. However, there is now an infinite ambiguity in the relation between $τ^0_{eff}$ and $τ$ and between $\tilde{u}$ and $u$, corresponding to an infinite number of unknown coefficients in the instanton expansion. Thus the reinterpreted curve (unlike the cases N_F<4) no longer determines the quantum modulus u as a function of the classical VEV a.

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arXiv1996

Multi-Instanton Calculus in N=2 Supersymmetric Gauge Theory II: Coupling to Matter

We further discuss the N=2 superinstantons in SU(2) gauge theory, obtained from the general self-dual solutions of topological charge n constructed by Atiyah, Drinfeld, Hitchin and Manin (ADHM). We realize the N=2 supersymmetry algebra as actions on the superinstanton moduli. This allows us to recast in concise superfield notation our previously obtained expression for the exact classical interaction between n ADHM superinstantons mediated by the adjoint Higgs bosons, and moreover, to incorporate N_F flavors of hypermultiplets. We perform explicit 1- and 2-instanton checks of the Seiberg-Witten prepotentials for all N_F and arbitrary hypermultiplet masses. Our results for the low-energy couplings are all in precise agreement with the predictions of Seiberg and Witten except for N_F=4, where we find a finite renormalization of the coupling which is absent in the proposed solution.

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arXiv1996

A Two-Instanton Test of the Exact Solution of N=2 Supersymmetric QCD

The exact solution of N=2 supersymmetric QCD found by Seiberg and Witten includes a prediction for all multi-instanton contributions to the low-energy dynamics. In the case where the matter hypermultiplets are massless, the leading non-perturbative contribution at weak coupling comes from the two-instanton sector. We calculate this contribution from first principles using the exact two-instanton solution of the self-dual Yang-Mills equation found by Atiyah, Drinfeld, Hitchin and Manin. We find exact agreement with the predictions of Seiberg and Witten for all numbers of flavours. We also confirm their predictions for the case of massive hypermultiplets.

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