Klebanov-Strassler Background Research Articles

Glueballs on the baryonic branch of Klebanov-Strassler: dimensional deconstruction and a light scalar particle

Within gauge/gravity duality, we compute the scalar and tensor mass spectrum in the boundary theory defined by the five-dimensional sigma-model coupled to gravity obtained by constraining to eight scalars the truncation on T1,1 that corresponds to the Papadopoulos-Tseytlin (PT) ansatz. We study fluctuations around the 1-parameter family of backgrounds that lift to the baryonic branch of the Klebanov-Strassler (KS) system, and interpolates between the KS background and the Maldacena-Nunez one (CVMN). We adopt a gauge invariant formalism in the treatment of the fluctuations that we interpret as states of the dual theory. The tensor spectrum interpolates between the discrete spectrum of the KS background and the continuum spectrum of the CVMN background, in particular showing the emergence of a finite energy range containing a dense set of states, as expected from dimensional deconstruction. The scalar spectrum shows analogous features, and in addition it contains one state that becomes parametrically light far from the origin along the baryonic branch.

A goldstino at the bottom of the cascade

Working within a five-dimensional consistent truncation of type IIB supergravity dimensionally reduced on $T^{1,1}$, we consider supersymmetry breaking solutions with the asymptotics of the supersymmetric Klebanov-Strassler background. There exists a two-parameter family of such solutions. Within this family, we show that those (and only those) solutions related to antiD-branes at the tip of the conifold correspond to dual field theory vacua where a goldstino mode is present and supercurrent Ward identities hold. Our findings do not depend on the IR singularity of the dual backgrounds, nor on its resolution. As such, they constitute an independent, necessary check for the existence of supersymmetry breaking vacua in the conifold cascading gauge theory. Our analysis relies on a holographic derivation of the Ward identities which has a wider applicability, beyond the specific system and symmetries considered here.

Entanglement entropy of the Klebanov-Strassler model with dynamical flavors

We present a detailed study of the Entanglement Entropy for the confining Klebanov-Strassler background coupled to a large number of dynamical flavors in the Veneziano limit. As we vary the number of the massless flavors the behavior of the entropy strongly depends on the way we fix the integration constant of the warp factor, that is related to the glueball scale. In the case of massive flavors, the mass of the flavor branes introduces another scale in the background and the entropy undergoes two first order phase transitions. The competition between the glueball and the quark scales will lead to a critical point where one of the phase transitions degenerates to a second order one. We have calculated the critical exponents and have found that they are independent of the number of flavors and different from the mean field theory expectations.

Light scalar from deformations of the Klebanov-Strassler background

We study deformations of the Klebanov-Strassler background parametrized by the size of a dim-6 VEV. In the UV, these solutions describe the usual duality cascade of Klebanov-Strassler; however below the scale rho* set by the dim-6 VEV they exhibit hyperscaling violation over a range of the radial coordinate. Focusing on the spectrum of scalar glueballs, we find a parametrically light state, the mass of which is suppressed by rho*, becoming massless in the limit of rho* -> infinity. Along the way, we clarify the choice of IR and UV boundary conditions for the fluctuations in the bulk, and find agreement with previous calculations for the spectrum of Klebanov-Strassler.

Uplifting the baryonic branch: a test for backreacting anti-D3-branes

Placing D3 or anti-D3-branes at the tip of the Klebanov-Strassler background results in uplifting the baryonic branch of the moduli space of the dual field theory. In this paper we derive a mass formula for the scalar particle associated with the motion along the baryonic branch, from both open and closed string points of view. We show that both methods give the same mass at linear order in number of (anti)D3-branes, thus providing a comprehensive check for the recently found linearized supergravity solution describing backreacting anti-D3-branes at the tip.

Dualising the baryonic branch: Dynamic [formula omitted] and confining backgrounds in IIA

In this paper we construct and examine new supersymmetric solutions of massive IIA supergravity that are obtained using non-Abelian T-duality applied to the baryonic branch of the Klebanov–Strassler background. The geometries display SU(2) structure which we show flows from static in the UV to dynamic in the IR. Confinement and symmetry breaking are given a geometrical interpretation by this change of structure. Various field theory observables are studied, suggesting possible ways to break conformality and flow in N=1TN and related field theories.

The backreaction of anti-D3 branes on the Klebanov-Strassler geometry

Abstract We present the full numerical solution for the 15-dimensional space of linearized deformations of the Klebanov-Strassler background which preserve the SU(2) × SU(2) × $ {{\mathbb{Z}}_2} $ symmetries. We identify within this space the solution corresponding to anti-D3 branes, (modulo the presence of a certain “subleading” singularity in the infrared). All the 15 integration constants of this solution are fixed in terms of the number of anti-D3 branes, and the solution differs in the UV from the supersymmetric solution into which it is supposed to decay by a mode corresponding to a rescaling of the field theory coordinates. Deciding whether two solutions that differ in the UV by a rescaling mode are dual to the same theory is involved even for supersymmetric Klebanov-Strassler solutions, and we explain in detail some of the subtleties associated to this.

Antibranes cannot become black

When D-branes are inserted in flux backgrounds of opposite charge, the resulting solution has a certain singularity in the fluxes. Recently it has been argued, using numerical solutions, that for anti-D3 branes in the Klebanov-Strassler background, these singularities cannot be cloaked by a horizon, which strongly suggests they are not physical. In this paper we provide an analytic proof that the singularity of all codimension-three antibrane solutions (such as anti-D6 branes in massive type IIA supergravity or anti-D3 branes smeared on the ${\mathbb{T}}^{3}$ of ${\mathbb{R}}^{3}\ifmmode\times\else\texttimes\fi{}{\mathbb{T}}^{3}$ with fluxes) cannot be hidden behind a horizon and that the charge of black branes with smooth event horizons must have the same sign as the charge of the flux background. Our result indicates that infinitesimally blackening the antibranes immediately triggers brane-flux annihilation and strengthens the intuition that antibranes placed in flux with positive charge immediately annihilate against it.

Scalar and vector mesons of flavor chiral symmetry breaking in the Klebanov-Strassler background

Recently, Dymarsky, Kuperstein and Sonnenschein constructed an embedding of flavor D7- and anti-D7-branes in the Klebanov-Strassler geometry that breaks the supersymmetry of the background, yet is stable. In this article, we study in detail the spectrum of vector mesons in this new model of flavor chiral symmetry breaking and commence an analytical analysis of the scalar mesons in this setup.

Inflation on a Pair of a D3-brane and a D3-brane in the Klebanov-Strassler Background

The authors appreciate the helpful discussions with Akira Ishida, Taekyung Kim; and Jin Hyang Song. This work was supported by a Korea Research Foundation grant funded by the Korean Government with grant numbers KRF-2008-313-C00170 and 2011-0011660 (Y.K.), and by the research fund of Hanyang University (HY-2006-S) (H.B.K).

Attractive holographic baryons

We propose a holographic model of baryon interactions based on non-supersymmetric D7-anti-D7 flavor branes embedded in the Klebanov-Strassler background. The baryons are D3-branes wrapping the 3-sphere of the conifold with M strings connecting the D3 and the flavor branes. Depending on the location of the latter there are two possibilities: the D3 either remains separate from the flavor branes or dissolves in them and becomes a flavor instanton. The leading order interaction between the baryons is a competition between the attraction and the repulsion due to the sigma and omega mesons. The lightest 0++ particle sigma is a pseudo-Goldstone boson associated with the spontaneous breaking of scale invariance. In a certain range of parameters it is parametrically lighter than any other massive state. As a result at large distances baryons attract each other. At short distances the potential admits a repulsive core due to an exchange of the omega vector meson. We discuss baryon coupling to glueballs, massive mesons and pions and point out the condition for the model to have a small binding energy.

On vector meson masses in a holographic SQCD

We study probe flavor branes supersymmetrically embedded in the Klebanov-Strassler background. The embedding is controlled by a single complex parameter μ related to the quark mass. We study the spectrum of the vector mesons as a function of μ and compare it with the experimental data. Assuming that the ρ(2150) meson is a 3 3 S 1 mode we find a remarkable agreement with the masses of the lightest excited ρ-mesons. Also, for a certain range of parameters our model exhibits an unusual behavior. The mesons built of the lighter quarks become more heavy than the ones built of the heavier quarks. We comment on a possible connection this phenomenon may have with the masses of the putative pure strange-anti strange mesons.

On the existence of meta-stable vacua in Klebanov-Strassler

We solve for the complete space of linearized deformations of the Klebanov-Strassler background consistent with the symmetries preserved by a stack of anti-D3 branes smeared on the S 3 of the deformed conifold. We find that the only solution whose UV physics is consistent with that of a perturbation produced by anti-D3 branes must have a singularity in the infrared, coming from NS and RR three-form field strengths whose energy density diverges. If this singularity is admissible, our solution describes the backreaction of the anti-D3 branes, and is thus likely to be dual to the conjectured metastable vacuum in the Klebanov-Strassler field theory. If this singularity is not admissible, then our analysis strongly suggests that anti-D3 branes do not give rise to metastable Klebanov-Strassler vacua, which would have dramatic consequences for some string theory constructions of de Sitter space. Key to this result is a simple, universal form for the force on a probe D3-brane in our ansatz.

Chiral symmetry breaking with non-SUSY D7-branes in ISD backgrounds

Supersymmetric probe branes satisfy the κ-symmetry condition which ensures that the action is minimized with respect to both variations of the embedding and of the world-volume gauge field. We observe that the κ-symmetry condition for a D7-brane in an imaginary self-dual (ISD) background can be generalized yielding minimization of the action with respect to variations of the gauge field only but not of the embedding. This provides a new way to construct non-BPS solutions for D7-branes once the embedding extremizes the geometrical volume of the brane. We then apply this method to the Klebanov-Strassler background and find a new D7−7 brane configuration that realizes the spontaneous breaking of flavor chiral symmetry as evidenced by the Goldstone boson identified in the spectrum. This result generalizes our previous construction for the Klebanov-Witten model. We compare our setup with the Sakai-Sugimoto model and discuss possible applications to QCD-like physics.

On the effective action of confining strings

We study the low-energy effective action on confining strings (in the fundamental representation) in SU(N) gauge theories in D space-time dimensions. We write this action in terms of the physical transverse fluctuations of the string. We show that for any D, the four-derivative terms in the effective action must exactly match the ones in the Nambu-Goto action, generalizing a result of Luscher and Weisz for D=3. We then analyze the six-derivative terms, and we show that some of these terms are constrained. For D=3 this uniquely determines the effective action for closed strings to this order, while for D>3 one term is not uniquely determined by our considerations. This implies that for D=3 the energy levels of a closed string of length L agree with the Nambu-Goto result at least up to order 1/L^5. For any D we find that the partition function of a long string on a torus is unaffected by the free coefficient, so it is always equal to the Nambu-Goto partition function up to six-derivative order. For a closed string of length L, this means that for D>3 its energy can, in principle, deviate from the Nambu-Goto result at order 1/L^5, but such deviations must always cancel in the computation of the partition function. Next, we compute the effective action up to six-derivative order for the special case of confining strings in weakly-curved holographic backgrounds, at one-loop order (leading order in the curvature). Our computation is general, and applies in particular to backgrounds like the Witten background, the Maldacena-Nunez background, and the Klebanov-Strassler background. We show that this effective action obeys all of the constraints we derive, and in fact it precisely agrees with the Nambu-Goto action (the single allowed deviation does not appear).

ℐ-odd sector of the Klebanov-Strassler theory

The Klebanov-Strassler background is invariant under the 2 symmetry , which acts by exchanging the bi-fundamental fields A and B, accompanied by the charge conjugation. We study the background perturbations in the -odd sector and find an exhaustive list of bosonic states invariant under the global SU(2) × SU(2) symmetry. In addition to the scalars identified in an earlier publication arXiv: 0712.4404 we find 7 families of massive states of spin 1. Together with the spin 0 states they form 3 families of massive vector multiplets and 2 families of massive gravitino multiplets, containing a vector, a pseudovector and fermions of spin 3/2 and 1/2. In the conformal Klebanov-Witten case these -odd particles belong to the = 1 superconformal Vector Multiplet I and Gravitino Multiplets II and IV. The operators dual to the -odd singlet sector include those without bi-fundamental fields making an interesting connection with the pure = 1 SYM theory. We calculate the mass spectrum of the corresponding glueballs numerically and discuss possible applications of our results.

UV-divergences of Wilson loops for gauge/gravity duality

We analyze the structure of the UV divergences of the Wilson loop for a general gauge/gravity duality. We find that, due to the presence of a nontrivial NSNS B-field and metric, new divergences that cannot be subtracted out by the conventional Legendre transform may arise. We also derive conditions on the B-field and the metric, which when satisfied, the leading UV divergence will become linear, and can be cancelled out by choosing the boundary condition of the string appropriately. Our results, together with the recent result of arXiv:0807.5127, where the effect of a nontrivial dilaton on the structure of UV divergences in Wilson loop is analysed, allow us to conclude that Legendre transform is at best capable of cancelling the linear UV divergences arising from the area of the worldsheet, but is incapable to handle the divergences associated with the dilaton or the B-field in general. We also solve the conditions for the cancellation of the leading linear divergences generally and find that many well-known supergravity backgrounds are of these kinds, including examples such as the Sakai-Sugimoto QCD model or N=1 duality with Sasaki-Einstein spaces. We also point out that Wilson loop in the Klebanov-Strassler background have a divergence associated with the B-field which cannot be cancelled away with the Legendre transform. Finally we end with some comments on the form of the Wilson loop operator in the ABJM superconformal Chern-Simons theory.

Conifolds and geometric transitions

Conifold geometries have recieved much attention in string theory and string-inspired cosmology recently, in particular the Klebanov-Strassler background that is known as the ''warped throat.'' This paper provides a pedagogical explanation for the singularity resolution in this geometry and emphasizes its connection to geometric transitions. The first part focuses on the gauge theory dual to the Klebanov-Strassler background, including the T-dual intersecting branes description. Then, a connection to the Gopakumar-Vafa conjecture for open-closed string duality is presented and a series of papers verifying this model on the supergravity level is summarized. An appendix provides extensive background material about conifold geometries. Special attention is given to their complex structures and the supersymmetry conditions on the background flux in constructions with fractional D3-branes on the singular (Klebanov-Tseytlin) and resolved (Pando Zayas-Tseytlin) conifolds are reevaluated. In agreement with earlier results, it is shown that only the singular solution allows a supersymmetric flux. However, the importance of using the correct complex structure to reach this conclusion is emphasized.

Kaluza-Klein relics from warped reheating

It has been suggested that after brane-antibrane inflation in a Klebanov-Strassler (KS) warped throat, metastable Kaluza-Klein (KK) excitations can be formed due to nearly-conserved angular momenta along isometric directions in the throat. If sufficiently long-lived, these relics could conflict with bigbang nucleosynthesis or baryogenesis by dominating the energy density of the universe. We make a detailed estimate of the decay rate of such relics using the low energy effective action of type IIB string theory compactified on the throat geometry, with attention to powers of the warp factor. We find that it is necessary to turn on SUSY-breaking deformations of the KS background in order to ensure that the most dangerous relics will decay fast enough. The decay rate is found to be much larger than the naive guess based on the dimension of the operators which break the angular isometries of the throat. For an inflationary warp factor of orderw ∼ 10 −4 , we obtain the boundM3/2 > ∼ 10 9 GeV on the scale of SUSY breaking to avoid cosmological problems from the relics, which is satisfied in the KKLT construction assumed to stabilize the compactification. Given the requirement that the relics decay before nucleosynthesis or baryogenesis, we place bounds on the mass of the relic as a function of the warp factor in the throat for more general warped backgrounds.

The mesonic branch of the deformed conifold

Using coordinates that manifest the S2-S3 split of the base, we study D3-branes localized on the three-sphere in the Klebanov-Strassler background. We find a numerical solution for the warp factor and show the emergence of the AdS throat near the stack. In the dual gauge theory, this corresponds to an RG flow along the mesonic branch. We demonstrate how the cubic superpotential of the = 4 SYM theory emerges at the end of the RG flow.