arXiv subjects

Nicholas P. Warner

Publications and source records attributed to Nicholas P. Warner.

105 records · Page 6Linked to original sources

arXiv2003

Effective Superpotentials, Geometry and Integrable Systems

We consider the effective superpotentials of N=1 SU(N_c) and U(N_c) supersymmetric gauge theories that are obtained from the N=2 theory by adding a tree-level superpotential. We show that several of the techniques for computing the effective superpotential are implicitly regularized by 2N_c massive fundamental quarks, i.e. the theory is embedded in the finite theory with nontrivial UV fixed point. In order to study N=1 and N=2 theories with fundamentals, we explicitly factorize the Seiberg-Witten curve for N_f != 0 and compare to the known form of the N=1 superpotential. N=2 gauge theories have an underlying integrable structure, and we obtain results on a new Lax matrix for N_f = N_c.

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arXiv2003

The Glueball Superpotential

We compute glueball superpotentials for four-dimensional, N=1 supersymmetric gauge theories, with arbitrary gauge groups and massive matter representations. This is done by perturbatively integrating out massive, charged fields. The Feynman diagram computations simplify, and are related to the corresponding matrix model. This leads to a natural notion of ``projection to planar diagrams'' for arbitrary gauge groups and representations. We discuss a general ambiguity in the glueball superpotential W(S) for terms, S^n, whose order, n, is greater than the dual Coxeter number. This ambiguity can be resolved for all classical gauge groups, (A,B,C,D), via a natural embedding in an infinite rank supergroup. We use this to address some recently raised puzzles. For exceptional groups, we compute the superpotential terms for low powers of the glueball field and propose an all-order completion for some examples including N=1^* for all simply-laced groups. We also comment on compactification of these theories to lower dimensions.

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arXiv2003

Generalizing the N=2 supersymmetric RG flow solution of IIB supergravity

We explicitly construct the supersymmetry transformations for the N=2 supersymmetric RG flow solution of chiral IIB supergravity. We show that the metric, dilaton/axion, five-index tensor and half of the three index tensor are determined algebraically in terms of the Killing spinor of the unbroken supersymmetry. The algebraic nature of the solution allows us to generalize this construction to a new class of N=2 supersymmetric solutions of IIB supergravity. Each solution in this class is algebraically determined by supersymmetry and is parametrized by a single function of two variables that satisfies a non-linear equation akin to the Laplace equation on the space transverse to the brane.

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arXiv2002

Flowing with Eight Supersymmetries in M-Theory and F-theory

We consider holographic RG flow solutions with eight supersymmetries and study the geometry transverse to the brane. For both M2-branes and for D3-branes in F-theory this leads to an eight-manifold with only a four-form flux. In both settings there is a natural four-dimensional hyper-Kahler slice that appears on the Coulomb branch. In the IIB theory this hyper-Kahler manifold encodes the Seiberg-Witten coupling over the Coulomb branch of a U(1) probe theory. We focus primarily upon a new flow solution in M-theory. This solution is first obtained using gauged supergravity and then lifted to eleven dimensions. In this new solution, the brane probes have an Eguchi-Hanson moduli space with the M2-branes spread over the non-trivial 2-sphere. It is also shown that the new solution is valid for a class of orbifold theories. We discuss how the hyper-Kahler structure on the slice extends to some form of G-structure in the eight-manifold, and describe how this can be computed.

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arXiv2002

Gauged Supergravity and Holographic Field Theory

This is a slightly expanded version of my talk at Future Perspectives in Theoretical Physics and Cosmology, Stephen Hawking's 60th Birthday Worshop. I describe some of the issues that were important in gauged supergravity in the 1980's and how these, and related issues have once again become important in the study of holographic field theories.

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arXiv2002

Orbifolds and Flows from Gauged Supergravity

We examine orbifolds of the IIB string via gauged supergravity. For the gravity duals of the A_{n-1} quiver gauge theories, we extract the massless degrees of freedom and assemble them into multiplets of N=4 gauged supergravity in five dimensions. We examine the embedding of the gauge group into the isometry group of the scalar manifold, as well as the symmetries of the scalar potential. From this we find that there is a large SU(1,n) symmetry group which relates different RG flows in the dual quiver gauge theory. We find that this symmetry implies an extension of the usual duality between ten-dimensional IIB solutions which involves exchanging geometric moduli with background fluxes.

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arXiv2001

An N = 2 Supersymmetric Membrane Flow

We find M-theory solutions that are holographic duals of flows of the maximally supersymmetric N=8 scalar-fermion theory in (2+1) dimensions. In particular, we construct the M-theory solution dual to a flow in which a single chiral multiplet is given a mass, and the theory goes to a new infra-red fixed point. We also examine this new solution using M2-brane probes. The (2+1)-dimensional field theory fixed-point is closely related to that of Leigh and Strassler, while the M-theory solution is closely related to the corresponding IIB flow solution. We recast the IIB flow solution in a more geometric manner and use this to obtain an Ansatz for the M-theory flow. We are able to generalize our solution further to obtain flows with del Pezzo sub-manifolds, and we give an explicit solution with a conifold singularity.

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arXiv2001

An N=1 Supersymmetric Coulomb Flow

We find a three-parameter family of solutions to IIB supergravity that corresponds to N=1 supersymmetric holographic RG flows of N=4 supersymmetric Yang Mills theory. This family of solutions allows one to give a mass to a single chiral superfield, and to probe a two-dimensional subspace of the Coulomb branch. In particular, we examine part of the Coulomb branch of the Leigh-Strassler fixed point. We look at the infra-red asymptotics of these flows from the ten-dimensional perspective. We also make general conjectures for the lifting Ansatz of five-dimensional scalar configurations to ten-dimensional tensor gauge fields. Our solution provides a highly non-trivial test of these conjectures.

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arXiv2001

ADE Singularities and Coset Models

We consider the compactification of the IIA string to (1+1) dimensions on non-compact 4-folds that are ALE fibrations. Supersymmetry requires that the compactification include 4-form fluxes, and a particular class of these models has been argued by Gukov, Vafa and Witten to give rise to a set of perturbed superconformal coset models that also have a Landau-Ginzburg description. We examine all these ADE models in detail, including the exceptional cosets. We identify which perturbations are induced by the deformation of the singularity, and compute the Landau-Ginzburg potentials exactly. We also show how the the Landau-Ginzburg fields and their superpotentials arise from the geometric data of the singularity, and we find that this is most naturally described in terms of non-compact, holomorphic 4-cycles.

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arXiv2000

Holographic Renormalization Group Flows: The View from Ten Dimensions

The holographic description of supersymmetric RG flows in supergravity is considered from both the five-dimensional and ten-dimensional perspectives. An N=1* flow of N=4 super-Yang Mills is considered in detail, and the infra-red limit is studied in terms of IIB supergravity in ten dimensions. Depending on the vevs and the direction of approach to the core, the supergravity solution can be interpreted in terms of either 5-branes or 7-branes. Generally, it is shown that it is essential to use the ten-dimensional description in order to study the infra-red asymptotics in supergravity.

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arXiv2000

N=1 Supersymmetric Renormalization Group Flows from IIB Supergravity

We consider N=1 supersymmetric renormalization group flows of N=4 Yang-Mills theory from the perspective of ten-dimensional IIB supergravity. We explicitly construct the complete ten-dimensional lift of the flow in which exactly one chiral superfield becomes massive (the LS flow). We also examine the ten-dimensional metric and dilaton configurations for the ``super-QCD'' flow (the GPPZ flow) in which all chiral superfields become massive. We show that the latter flow generically gives rise to a dielectric 7-brane in the infra-red, but the solution contains a singularity that may be interpreted as a ``duality averaged'' ring distribution of 5-branes wrapped on S^2. At special values of the parameters the singularity simplifies to a pair of S-dual branes with (p,q) charge (1,\pm 1).

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arXiv2000

A Class of N=1 Supersymmetric RG Flows from Five-dimensional N = 8 Supergravity

We consider the holographic dual of a general class of N=1* flows in which all three chiral multiplets have independent masses, and in which the corresponding Yang-Mills scalars can develop particular supersymmetry-preserving vevs. We also allow the gaugino to develop a vev. This leads to a six parameter subspace of the supergravity scalar action, and we show that this is a consistent truncation, and obtain a superpotential that governs the N=1* flows on this subspace. We analyse some of the structure of the superpotential, and check consistency with the asymptotic behaviour near the UV fixed point. We show that the dimensions of the six couplings obey a sum rule all along the N=1* flows. We also show how our superpotential describes part of the Coulomb branch of the non-trivial N=1 fixed point theory.

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arXiv2000

A New Supersymmetric Compactification of Chiral IIB Supergravity

We present a new compactification of chiral, N=2 ten-dimensional supergravity down to five dimensions and show that it corresponds to the N=2 supersymmetric critical point of five-dimensional, N=8 gauged supergravity found in [KPW]. This solution presented here is of particular significance because it involves non-zero tensor gauge fields and, via the AdS/CFT correspondence, is dual to the non-trivial N=1 supersymmetric fixed point of N=4 Yang-Mills theory.

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arXiv2000

N=2 Supersymmetric RG Flows and the IIB Dilaton

We show that there is a non-trivial relationship between the dilaton of IIB supergravity, and the coset of scalar fields in five-dimensional, gauged N=8 supergravity. This has important consequences for the running of the gauge coupling in massive perturbations of the AdS/CFT correspondence. We conjecture an exact analytic expression for the ten-dimensional dilaton in terms of five-dimensional quantities, and we test this conjecture. Specifically, we construct a family of solutions to IIB supergravity that preserve half of the supersymmetries, and are lifts of supersymmetric flows in five-dimensional, gauged N=8 supergravity. Via the AdS/CFT correspondence these flows correspond to softly broken N=4, large N Yang-Mills theory on part of the Coulomb branch of N=2 supersymmetric Yang-Mills. Our solutions involve non-trivial backgrounds for all the tensor gauge fields as well as for the dilaton and axion.

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arXiv1997

BPS Geodesics in N=2 Supersymmetric Yang-Mills Theory

We introduce some techniques for making a more global analysis of the existence of geodesics on a Seiberg-Witten Riemann surface with metric $ds^2 = |λ_{SW}|^2$. Because the existence of such geodesics implies the existence of BPS states in N=2 supersymmetric Yang-Mills theory, one can use these methods to study the BPS spectrum in various phases of the Yang-Mills theory. By way of illustration, we show how, using our new methods, one can easily recover the known results for the N=2 supersymmetric SU(2) pure gauge theory, and we show in detail how it also works for the N=2, SU(2) theory coupled to a massive adjoint matter multiplet.

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