arXiv subjects

Heng-Yu Chen

Publications and source records attributed to Heng-Yu Chen.

At least 55 records · Page 3Linked to original sources

arXiv2012

A 5d/3d duality from relativistic integrable system

We propose and prove a new exact duality between the F-terms of supersymmetric gauge theories in five and three dimensions with adjoint matter fields. The theories are compactified on a circle and are subject to the Omega deformation. In the limit proposed by Nekrasov and Shatashvili, the supersymmetric vacua become isolated and are identified with the eigenstates of a quantum integrable system. The effective twisted superpotentials are the Yang-Yang functional of the relativistic elliptic Calogero-Moser model. We show that they match on-shell by deriving the Bethe ansatz equation from the saddle point of the five-dimensional partition function. We also show that the Chern-Simons terms match and extend our proposal to the elliptic quiver generalizations.

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arXiv2011

A New 2d/4d Duality via Integrability

We prove a duality, recently conjectured in arXiv:1103.5726, which relates the F-terms of supersymmetric gauge theories defined in two and four dimensions respectively. The proof proceeds by a saddle point analysis of the four-dimensional partition function in the Nekrasov-Shatashvili limit. At special quantized values of the Coulomb branch moduli, the saddle point condition becomes the Bethe Ansatz Equation of the SL(2) Heisenberg spin chain which coincides with the F-term equation of the dual two-dimensional theory. The on-shell values of the superpotential in the two theories are shown to coincide in corresponding vacua. We also identify two-dimensional duals for a large set of quiver gauge theories in four dimensions and generalize our proof to these cases.

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arXiv2011

Moduli Space and Wall-Crossing Formulae in Higher-Rank Gauge Theories

We study the interplay between wall-crossing in four-dimensional gauge theory and instanton contributions to the moduli space metric of the same theory on $\mathbb{R}^{3}\times S^{1}$. We consider $\mathcal{N}=2$ SUSY Yang--Mills with gauge group SU(n) and focus on walls of marginal stability which extend to weak coupling. By comparison with explicit field theory results we verify the Kontsevich--Soibelman formula for the change in the BPS spectrum at these walls and check the smoothness of the metric in the corresponding compactified theory. We also verify in detail the predictions for the one instanton contribution to the metric coming from the non-linear integral equations of Gaiotto, Moore and Nietzke.

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arXiv2010

Towards multi-field D-brane inflation in a warped throat

We study the inflationary dynamics in a model of slow-roll inflation in warped throat. Inflation is realized by the motion of a D-brane along the radial direction of the throat, and at later stages instabilities develop in the angular directions. We closely investigate both the single field potential relevant for the slow-roll phase, and the full multi-field one including the angular modes which becomes important at later stages. We study the main features of the instability process, discussing its possible consequences and identifying the vacua towards which the angular modes are driven.

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arXiv2010

Notes on Wall Crossing and Instanton in Compactified Gauge Theory with Matter

We study the quantum effects on the Coulomb branch of N=2 SU(2) supersymmetric Yang-Mills with fundamental matters compactified on R^3 x S^1, and extract the explicit perturbative and leading non-perturbative corrections to the moduli space metric predicted from the recent work of Gaiotto, Moore and Neitzke on wall-crossing [1]. We verify the predicted metric by computing the leading weak coupling instanton contribution to the four fermion correlation using standard field theory techniques, and demonstrate perfect agreement. We also demonstrate how previously known three dimensional quantities can be recovered in appropriate small radius limit, and provide a simple geometric picture from brane construction.

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arXiv2010

Wall Crossing and Instantons in Compactified Gauge Theory

We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group SU(2) compactified on R^3 x S^1. The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.

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arXiv2009

On Supersymmetric D7-branes in the Warped Deformed Conifold

We study the supersymmetric properties of D7-branes in the warped deformed conifold. We consider the $κ$-symmetry conditions on D7-branes in this specific warped background, taking into account the background NS-NS 2-form flux. While any holomorphic embedding defines a supersymmetric D7-brane in the absence of background H-flux, most of the D7-brane embeddings considered in the literature do not preserve supersymmetry for the warped deformed conifold without also including brane worldvolume flux. For the simplest such embedding, we construct numerically the worldvolume fluxnecessary to restore supersymmetry. We also comment on the dual field theory descriptions in terms of cascading N=1 supersymmetric gauge theories with flavors. Finally, we discuss some possible applications of our results to moduli stabilization and vacuum energy uplifting, gauge/gravity duality, and string inflationary model building.

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arXiv2009

Towards a Holographic Model of Color-Flavor Locking Phase

We demonstrate a holographic realization of color-flavor locking phase, using N=4 SU(Nc) SYM coupled to N=2 Nf fundamental hypermultiplets as an example. The gravity dual consists of Nc D3-branes and Nf D7-branes with world volume gauge field representing the baryon density. Treating a small number \tilde{N}c << Nc of D3-branes as Yang-Mills instantons on the D7-branes, we consider possible potential(s) on their moduli space or equivalently the Higgs branch. We show that a non-trivial potential can be generated by including the backreaction of the baryonic density on the D7-branes, this dynamically drives the instantons (= D3-branes) into dissolution. We interpret this as a color-flavor locking since the size of the instanton is the squark vev, and study the symmetry breaking patterns. Extending to finite temperature setup, we demonstrate that color-flavor locking persists, and the thermal effect provides additional structures in the phase diagram.

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arXiv2009

Towards a warped inflationary brane scanning

We present a detailed systematics for comparing warped brane inflation with the observations, incorporating the effects of both moduli stabilization and ultraviolet bulk physics. We explicitly construct an example of the inflaton potential governing the motion of a mobile D3 brane in the entire warped deformed conifold. This allows us to precisely identify the corresponding scales of the cosmic microwave background. The effects due to bulk fluxes or localized sources are parametrized using gauge/string duality. We next perform some sample scannings to explore the parameter space of the complete potential, and first demonstrate that without the bulk effects there can be large degenerate sets of parameters with observationally consistent predictions. When the bulk perturbations are included, however, the observational predictions are generally spoiled. For them to remain consistent, the magnitudes of the bulk effects need to be highly suppressed via fine tuning.

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arXiv2009

On D3-brane Dynamics at Strong Warping

We study the dynamics of a D3 brane in generic IIB warped compactifications, using the Hamiltonian formulation discussed in arXiv:0805.3700 [hep-th]. Taking into account of both closed and open string fluctuations, we derive the warped Kahler potential governing the motion of a probe D3 brane. By including the backreaction of D3, we also comment on how the problem of defining a holomorphic gauge coupling on wrapped D7 branes in warped background can be resolved.

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arXiv2009

Inflation on an Open Racetrack

We present a variant of warped D-brane inflation by incorporating multiple sets of holomorphically-embedded D7-branes involved in moduli stabilization with extent into a warped throat. The resultant D3-brane motion depends on the D7-brane configuration and the relative position of the D3-brane in these backgrounds. The non-perturbative moduli stabilization superpotential takes the racetrack form, but the additional D3-brane open string moduli dependence provides more flexibilities in model building. For concreteness, we consider D3-brane motion in the warped deformed conifold with the presence of multiple D7-branes, and derive the scalar potential valid for the entire throat. By explicit tuning of the microphysical parameters, we obtain inflationary trajectories near an inflection point for various D7-brane configurations. Moreover, the open racetrack potential admits approximate Minkowski vacua before uplifting. We demonstrate with a concrete D-brane inflation model where the Hubble scale during inflation can exceed the gravitino mass. Finally, the multiple sets of D7-branes present in this open racetrack setup also provides a mechanism to stabilize the D3-brane to metastable vacua in the intermediate region of the warped throat.

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arXiv2008

Systematics of multi-field effects at the end of warped brane inflation

We investigate in the context of brane inflation the possibility of additional light scalar fields generating significant power spectrum and non-Gaussianities at the end of inflation affecting the CMB scale observations. We consider the specific mechanism outlined by Lyth and describe the necessary criteria for it to be potentially important in a warped throat. We also discuss different mechanisms for uplifting the vacuum energy which can lead to different dominant contributions of the inflaton potential near the end of inflation. We then apply such criteria to one of the most detailed brane inflation models to date, and show that inflation can persist towards the tip of the throat, however for the specific stable inflationary trajectory, the light residual isometry direction becomes degenerate. We also estimate the effects for other inflationary trajectories with non-degenerate residual isometries.

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arXiv2008

Comments on the Boundary Scattering Phase

We present a simple solution to the crossing equation for an open string worldsheet reflection matrix, with boundaries preserving a SU(1|2)^2 residual symmetry, which constrains the boundary dressing factor. In addition, we also propose an analogous crossing equation for the dressing factor where extra boundary degrees of freedom preserve a SU(2|2)^2 residual symmetry.

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arXiv2007

Quantum Scattering of Giant Magnons

We perform a first-principles semi-classical computation of the one-loop corrections to the dispersion relation and S-matrix of Giant Magnons in AdS_5 x S^5 string theory. The results agree exactly with expectations based on the strong coupling expansion of the exact Asymptotic Bethe Ansatz equations. In particular we reproduce the Hernandez-Lopez term in the dressing phase.

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arXiv2007

Geometry and topology of bubble solutions from gauge theory

We study how geometrical and topological aspects of certain 1/2 BPS type IIB supergravity solutions are captured by the N=4 Super Yang-Mills gauge theory in the AdS/CFT context. The type IIB solutions are completely characterized by arbitrary droplets in a plane and we consider, in particular, concentric droplets. We probe the dual 1/2 BPS operators of the gauge theory with single traces and extract their one-loop anomalous dimensions. The action of the one-loop dilatation operator can be reformulated as the Hamiltonian of a bosonic lattice. The operators defining the Hamiltonian encode the topology of the droplet. The axial symmetry of the droplets turns out to be essential for obtaining the spectrum of the Hamiltonians. In appropriate BMN limits, the near-BPS spectrum reproduces the spectrum of near-BPS string excitations propagating along each individual edge of the droplet of the dual geometric background. We also study semiclassical regimes for the Hamiltonians. We show that for droplets having disconnected constituents, the Hamiltonian admits different complimentary semiclassical descriptions, each one replicating the semiclassical description for closed strings extending in each of the constituents.

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arXiv2006

The Asymptotic Spectrum of the N=4 Super Yang-Mills Spin Chain

In this paper we discuss the asymptotic spectrum of the spin chain description of planar N=4 SUSY Yang-Mills. The states appearing in the spectrum belong to irreducible representations of the unbroken supersymmetry SU(2|2) x SU(2|2) with non-trivial extra central extensions. The elementary magnon corresponds to the bifundamental representation while boundstates of Q magnons form a certain short representation of dimension 16Q^{2}. Generalising the Beisert's analysis of the Q=1 case, we derive the exact dispersion relation for these states by purely group theoretic means.

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arXiv2006

The Shape of Instantons : Cross-Section of Supertubes and Dyonic Instantons

We explore the correspondence between Yang-Mills instantons and algebraic curves. The curve is defined by Higgs zero locus of dyonic instantons in 1+4 dimensional Yang-Mills-Higgs theory, and it is identified in string theory with the cross-section of supertubes connecting parallel D4-branes. To present evidence for the identification, we show that with total charges fixed, the supertube angular momentum computed from the Higgs zero locus is maximized when the locus is circular, which has been proven for the cross-section of the supertubes. This leads to a consistent dictionary between the charges in two pictures. We also consider a T-dual version of the story, identifying the profiles of the wavy instanton strings with those of the supercurves/D-helices. Based on this observation, we then argue a novel correspondence between ADHM data of instantons and algebraic curves defining the locus. The degree of the curve is related to the instanton number, and splitting property of the curve is physically manifested by well-separated instantons.

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arXiv2006

On the Scattering of Magnon Boundstates

We study the scattering of magnon boundstates in the spin-chain description of planar N=4 SUSY Yang-Mills. Starting from the conjectured exact S-matrix for magnons in the SU(2) sector, we calculate the corresponding S-matrix for boundstates with an arbitrary number of constituent magnons. The resulting expression has an interesting analytic structure with both simple and double poles. We also calculate the semiclassical S-matrix for the scattering of the corresponding excitations on the string worldsheet known as Dyonic Giant Magnons. We find precise agreement with the magnon boundstate S-matrix in the limit of large 't Hooft coupling.

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