arXiv subjects

Christopher P. Herzog

Publications and source records attributed to Christopher P. Herzog.

At least 91 records · Page 5Linked to original sources

arXiv2006

Brane Tilings and Exceptional Collections

Both brane tilings and exceptional collections are useful tools for describing the low energy gauge theory on a stack of D3-branes probing a Calabi-Yau singularity. We provide a dictionary that translates between these two heretofore unconnected languages. Given a brane tiling, we compute an exceptional collection of line bundles associated to the base of the non-compact Calabi-Yau threefold. Given an exceptional collection, we derive the periodic quiver of the gauge theory which is the graph theoretic dual of the brane tiling. Our results give new insight to the construction of quiver theories and their relation to geometry.

hep-th↗

arXiv2006

Exceptional collections and D-branes probing toric singularities

We demonstrate that a strongly exceptional collection on a singular toric surface can be used to derive the gauge theory on a stack of D3-branes probing the Calabi-Yau singularity caused by the surface shrinking to zero size. A strongly exceptional collection, i.e., an ordered set of sheaves satisfying special mapping properties, gives a convenient basis of D-branes. We find such collections and analyze the gauge theories for weighted projective spaces, and many of the Y^{p,q} and L^{p,q,r} spaces. In particular, we prove the strong exceptionality for all p in the Y^{p,p-1} case, and similarly for the Y^{p,p-2r} case.

hep-th↗

arXiv2004

Symmetry Breaking and Axionic Strings in the Warped Deformed Conifold

We interpret D-strings at the bottom of the warped deformed conifold as axionic strings in the dual cascading SU(N+M) x SU(N) gauge theory. The axion is a massless pseudo-scalar glueball which we find in the supergravity fluctuation spectrum and interpret as the Goldstone boson of spontaneously broken U(1) baryon number symmetry. The existence of this massless glueball, anticipated in hep-th/0101013, supports the idea that the cascading gauge theory is on the baryonic branch, i.e. the U(1)_B global symmetry is broken by expectation values of baryonic operators. We also find a massless scalar glueball, which is a superpartner of the pseudo-scalar. This scalar mode is a mixture of an NS-NS 2-form and a metric perturbation of the warped deformed conifold of a type first considered in hep-th/0012034.

hep-th↗

arXiv2004

Variations on the Warped Deformed Conifold

The warped deformed conifold background of type IIB theory is dual to the cascading $SU(M(p+1))\times SU(Mp)$ gauge theory. We show that this background realizes the (super-)Goldstone mechanism where the U(1) baryon number symmetry is broken by expectation values of baryonic operators. The resulting massless pseudo-scalar and scalar glueballs are identified in the supergravity spectrum. A D-string is then dual to a global string in the gauge theory. Upon compactification, the Goldstone mechanism turns into the Higgs mechanism, and the global strings turn into ANO strings.

hep-th↗

arXiv2004

Seiberg Duality is an Exceptional Mutation

The low energy gauge theory living on D-branes probing a del Pezzo singularity of a non-compact Calabi-Yau manifold is not unique. In fact there is a large equivalence class of such gauge theories related by Seiberg duality. As a step toward characterizing this class, we show that Seiberg duality can be defined consistently as an admissible mutation of a strongly exceptional collection of coherent sheaves.

hep-th↗

arXiv2004

No-soliton--soliton phase transition in a trapped one-dimensional Bose gas

Following the experimental observation of bright matter-wave solitons [L. Khaykovich et al., Science v. 296, 1290 (2002); K. E. Strecker et al., Nature (London) v. 417, 150 (2002)], we develop a semi-phenomenological theory for soliton thermodynamics and find the condensation temperature. Under a modified thermodynamic limit, the condensate occupation at the critical temperature undergoes a sudden jump to a nonzero value, indicating a discontinuous phase transition. Treating the condensation as a diffusion over a barrier shows that the condensation time is exponentially long as one approaches the thermodynamic limit, and the longest near the critical temperature.

cond-mat.soft↗

arXiv2004

Exceptional Collections and del Pezzo Gauge Theories

Stacks of D3-branes placed at the tip of a cone over a del Pezzo surface provide a way of geometrically engineering a small but rich class of gauge/gravity dualities. We develop tools for understanding the resulting quiver gauge theories using exceptional collections. We prove two important results for a general quiver gauge theory: 1) we show the ordering of the nodes can be determined up to cyclic permutation and 2) we derive a simple formula for the ranks of the gauge groups (at the conformal point) in terms of the numbers of bifundamentals. We also provide a detailed analysis of four node quivers, examining when precisely mutations of the exceptional collection are related to Seiberg duality.

hep-th↗

arXiv2003

Remarks on the Warped Deformed Conifold

We assemble a few remarks on the supergravity solution of hep-th/0007191, whose UV asymptotic form was previously found in hep-th/0002159. First, by normalizing the R-R fluxes, we compare the logarithmic flow of couplings in supergravity with that in field theory, and find exact agreement. We also write the 3-form field strength $G_3 = F_3 - τH_3$ present in the solution in a manifestly SO(4) invariant (2,1) form. In addition, we discuss various issues related to the chiral symmetry breaking and wrapped branes.

hep-th↗

arXiv2003

Dibaryon Spectroscopy

The AdS/CFT correspondence relates dibaryons in superconformal gauge theories to holomorphic curves in Kaehler-Einstein surfaces. The degree of the holomorphic curves is proportional to the gauge theory conformal dimension of the dibaryons. Moreover, the number of holomorphic curves should match, in an appropriately defined sense, the number of dibaryons. Using AdS/CFT backgrounds built from the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999), we show that the gauge theory prediction for the dimension of dibaryonic operators does indeed match the degree of the corresponding holomorphic curves. For AdS/CFT backgrounds built from cones over del Pezzo surfaces, we are able to match the degree of the curves to the conformal dimension of dibaryons for the n'th del Pezzo surface, n=1,2,...,6. Also, for the del Pezzos and the A_k type generalized conifolds, for the dibaryons of smallest conformal dimension, we are able to match the number of holomorphic curves with the number of possible dibaryon operators from gauge theory.

hep-th↗

arXiv2003

Dibaryons from Exceptional Collections

We discuss aspects of the dictionary between brane configurations in del Pezzo geometries and dibaryons in the dual superconformal quiver gauge theories. The basis of fractional branes defining the quiver theory at the singularity has a K-theoretic dual exceptional collection of bundles which can be used to read off the spectrum of dibaryons in the weakly curved dual geometry. Our prescription identifies the R-charge R and all baryonic U(1) charges Q_I with divisors in the del Pezzo surface without any Weyl group ambiguity. As one application of the correspondence, we identify the cubic anomaly tr R Q_I Q_J as an intersection product for dibaryon charges in large-N superconformal gauge theories. Examples can be given for all del Pezzo surfaces using three- and four-block exceptional collections. Markov-type equations enforce consistency among anomaly equations for three-block collections.

hep-th↗

arXiv2003

The Sound of M-Theory

We consider sound propagation on M5- and M2-branes in the hydrodynamic limit. In particular, we look at the low energy description of a stack of N M-branes at finite temperature. At low energy, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. From this gravitational description, we calculate Lorentzian signature two-point functions of the stress-energy tensor on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit. The poles in these Green's functions show evidence for sound propagation in the field theory living on the M-branes.

hep-th↗

arXiv2003

The Hydrodynamics of M-Theory

We consider the low energy limit of a stack of N M-branes at finite temperature. In this limit, the M-branes are well described, via the AdS/CFT correspondence, in terms of classical solutions to the eleven dimensional supergravity equations of motion. We calculate Minkowski space two-point functions on these M-branes in the long-distance, low-frequency limit, i.e. the hydrodynamic limit, using the prescription of Son and Starinets [hep-th/0205051]. From these Green's functions for the R-currents and for components of the stress-energy tensor, we extract two kinds of diffusion constant and a viscosity. The N dependence of these physical quantities may help lead to a better understanding of M-branes.

hep-th↗

arXiv2002

On String Tensions in Supersymmetric SU(M) Gauge Theory

In some models of N=1 supersymmetric SU(M) gauge dynamics (hep-th/9503163 and hep-th/9707244), the tension of a string ending on q external quarks is proportional to sin(pi q/M), q=1,..., M-1. In this paper we calculate the ratios of the q-string tensions using the recently derived type IIB gravity duals of N=1 SUSY gauge theories. Far in the IR these gravity duals contain a three-sphere with M units of R-R 3-form flux which, upon S-duality, turns into NS-NS 3-form flux. The confining q-string is described by a D3-brane wrapping a two-sphere inside the three-sphere with q units of world volume flux. For one of the gravity dual backgrounds (Maldacena-Nunez) a D3-brane probe calculation exactly reproduces the sin(pi q/M) dependence, while for another (Klebanov-Strassler) we find approximate agreement. We speculate on the connection of the q-string tensions with D-brane tensions in the SU(2) WZW model.

hep-th↗

arXiv2002

D-Branes on the Conifold and N=1 Gauge/Gravity Dualities

We review extensions of the AdS/CFT correspondence to gauge/ gravity dualities with N=1 supersymmetry. In particular, we describe the gauge/gravity dualities that emerge from placing D3-branes at the apex of the conifold. We consider first the conformal case, with discussions of chiral primary operators and wrapped D-branes. Next, we break the conformal symmetry by adding a stack of partially wrapped D5-branes to the system, changing the gauge group and introducing a logarithmic renormalization group flow. In the gravity dual, the effect of these wrapped D5-branes is to turn on the flux of 3-form field strengths. The associated RR 2-form potential breaks the U(1) R-symmetry to $Z_{2M}$ and we study this phenomenon in detail. This extra flux also leads to deformation of the cone near the apex, which describes the chiral symmetry breaking and confinement in the dual gauge theory.

hep-th↗

arXiv2002

String Tensions and Three Dimensional Confining Gauge Theories

In the context of gauge/gravity duality, we try to understand better the proposed duality between the fractional D2-brane supergravity solutions of (Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+1 dimensional gauge theory. Based on the similarities between this fractional D2-brane solution and D3-brane supergravity solutions with more firmly established gauge theory duals, we conjecture that a confining q-string in the 2+1 dimensional gauge theory is dual to a wrapped D4-brane. In particular, the D4-brane looks like a string in the gauge theory directions but wraps a S**3 in S**4 in the transverse geometry. For one of the supergravity solutions, we find a near quadratic scaling law for the tension: $T \sim q (N-q)$. Based on the tension, we conjecture that the gauge theory dual is SU(N) far in the infrared. We also conjecture that a quadratic or near quadratic scaling is a generic feature of confining 2+1 dimensional SU(N) gauge theories.

hep-th↗

arXiv2002

Baryon Spectra and AdS/CFT Correspondence

We provide a detailed map between wrapped D3-branes in Anti-de Sitter (AdS) backgrounds and dibaryon operators in the corresponding conformal field theory (CFT). The effective five dimensional action governing the dynamics of AdS space contains a $U(1)_R$ gauge field that mediates interactions between objects possessing R-charge. We show that the $U(1)_R$ charge of these wrapped D3-branes as measured by the gauge field matches the R-charge of the dibaryons expected from field theory considerations. We are able, through a careful probe brane calculation in an $AdS_5\times T^{1,1}$ background, to understand the exact relation between the mass of the wrapped D3-brane and the dimension of the corresponding dibaryon. We also make some steps toward matching the counting of dibaryon operators in the CFT with the ground states of a supersymmetric quantum mechanical system whose target space is the moduli space of D-branes. Finally, we discuss BPS excitations of the D3-brane and compare them with higher dimension operators in the CFT.

hep-th↗

arXiv2001

The Volume of some Non-spherical Horizons and the AdS/CFT Correspondence

We calculate the volumes of a large class of Einstein manifolds, namely Sasaki-Einstein manifolds which are the bases of Ricci-flat affine cones described by polynomial embedding relations in C^n. These volumes are important because they allow us to extend and test the AdS/CFT correspondence. We use these volumes to extend the central charge calculation of Gubser (1998) to the generalized conifolds of Gubser, Shatashvili, and Nekrasov (1999). These volumes also allow one to quantize precisely the D-brane flux of the AdS supergravity solution. We end by demonstrating a relationship between the volumes of these Einstein spaces and the number of holomorphic polynomials (which correspond to chiral primary operators in the field theory dual) on the corresponding affine cone.

hep-th↗

arXiv2001

Fractional D1-Branes at Finite Temperature

The supergravity dual of $N$ regular and $M$ fractional D1-branes on the cone over the Einstein manifold $Q^{1,1,1}$ has a naked singularity in the infrared. The supergravity dual of $N$ regular and $M$ fractional D3-branes on the conifold also has such a singularity. Buchel suggested and Gubser et al. have shown that in the D3-brane case, the naked singularity is cloaked by a horizon at a sufficiently high temperature. In this paper we derive the system of second-order differential equations necessary to find such a solution for $Q^{1,1,1}$. We also find solutions to this system in perturbation theory that is valid when the Hawking temperature of the horizon is very high.

hep-th↗