arXiv subjects

Igor R. Klebanov

Publications and source records attributed to Igor R. Klebanov.

At least 73 records · Page 4Linked to original sources

arXiv2011

F-Theorem without Supersymmetry

The conjectured F-theorem for three-dimensional field theories states that the finite part of the free energy on S^3 decreases along RG trajectories and is stationary at the fixed points. In previous work various successful tests of this proposal were carried out for theories with {\cal N}=2 supersymmetry. In this paper we perform more general tests that do not rely on supersymmetry. We study perturbatively the RG flows produced by weakly relevant operators and show that the free energy decreases monotonically. We also consider large N field theories perturbed by relevant double trace operators, free massive field theories, and some Chern-Simons gauge theories. In all cases the free energy in the IR is smaller than in the UV, consistent with the F-theorem. We discuss other odd-dimensional Euclidean theories on S^d and provide evidence that (-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1 this is the well-known g-theorem.

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arXiv2011

M-Branes and Metastable States

We study a supersymmetry breaking deformation of the M-theory background found in arXiv:hep-th/0012011. The supersymmetric solution is a warped product of R^{2,1} and the 8-dimensional Stenzel space, which is a higher dimensional generalization of the deformed conifold. At the bottom of the warped throat there is a 4-sphere threaded by \tilde{M} units of 4-form flux. The dual (2+1)-dimensional theory has a discrete spectrum of bound states. We add p anti-M2 branes at a point on the 4-sphere, and show that they blow up into an M5-brane wrapping a 3-sphere at a fixed azimuthal angle on the 4-sphere. This supersymmetry breaking state turns out to be metastable for p / \tilde{M} < 0.054. We find a smooth O(3)-symmetric Euclidean bounce solution in the M5-brane world volume theory that describes the decay of the false vacuum. Calculation of the Euclidean action shows that the metastable state is extremely long-lived. We also describe the corresponding metastable states and their decay in the type IIA background obtained by reduction along one of the spatial directions of R^{2,1}.

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arXiv2011

Towards the F-Theorem: N=2 Field Theories on the Three-Sphere

For 3-dimensional field theories with {\cal N}=2 supersymmetry the Euclidean path integrals on the three-sphere can be calculated using the method of localization; they reduce to certain matrix integrals that depend on the R-charges of the matter fields. We solve a number of such large N matrix models and calculate the free energy F as a function of the trial R-charges consistent with the marginality of the superpotential. In all our {\cal N}=2 superconformal examples, the local maximization of F yields answers that scale as N^{3/2} and agree with the dual M-theory backgrounds AdS_4 x Y, where Y are 7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local F-maximization is equivalent to the minimization of the volume of Y over the space of Sasakian metrics, a procedure also referred to as Z-minimization. Moreover, we find that the functions F and Z are related for any trial R-charges. In the models we study F is positive and decreases along RG flows. We therefore propose the "F-theorem" that we hope applies to all 3-d field theories: the finite part of the free energy on the three-sphere decreases along RG trajectories and is stationary at RG fixed points. We also show that in an infinite class of Chern-Simons-matter gauge theories where the Chern-Simons levels do not sum to zero, the free energy grows as N^{5/3} at large N. This non-trivial scaling matches that of the free energy of the gravity duals in type IIA string theory with Romans mass.

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arXiv2011

Multi-Matrix Models and Tri-Sasaki Einstein Spaces

Localization methods reduce the path integrals in {\cal N} >= 2 supersymmetric Chern-Simons gauge theories on S^3 to multi-matrix integrals. A recent evaluation of such a two-matrix integral for the {\cal N}=6 superconformal U(N) x U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, explaining, in particular the N^{3/2} scaling of the free energy. We study a class of p-matrix integrals describing {\cal N}=3 superconformal U(N)^p Chern-Simons gauge theories. We present a simple method that allows us to evaluate the eigenvalue densities and the free energies in the large N limit keeping the Chern-Simons levels k_i fixed. The dual M-theory backgrounds are AdS_4 x Y, where Y are seven-dimensional tri-Sasaki Einstein spaces specified by the k_i. The gravitational free energy scales inversely with the square root of the volume of Y. We find a general formula for the p-matrix free energies that agrees with the available results for volumes of the tri-Sasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS_4/CFT_3 dualities. This formula is consistent with the Seiberg duality conjectured for Chern-Simons gauge theories.

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arXiv2010

Green's Functions and Non-Singlet Glueballs on Deformed Conifolds

We study the Laplacian on Stenzel spaces (generalized deformed conifolds), which are tangent bundles of spheres endowed with Ricci flat metrics. The (2d-2)-dimensional Stenzel space has SO(d) symmetry and can be embedded in C^d through the equation \sum_{i = 1}^d {z_i^2} = ε^2. We discuss the Green's function with a source at a point on the S^{d-1} zero section of TS^{d-1}. Its calculation is complicated by mixing between different harmonics with the same SO(d) quantum numbers due to the explicit breaking by the ε-deformation of the U(1) symmetry that rotates z_i by a phase. A similar mixing affects the spectrum of normal modes of warped deformed conifolds that appear in gauge/gravity duality. We solve the mixing problem numerically to determine certain bound state spectra in various representations of SO(d) for the d=4 and d=5 examples.

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arXiv2010

Emergent Quantum Near-Criticality from Baryonic Black Branes

We find new black 3-brane solutions describing the "conifold gauge theory" at nonzero temperature and baryonic chemical potential. Of particular interest is the low-temperature limit where we find a new kind of weakly curved near-horizon geometry; it is a warped product AdS_2 x R^3 x T^{1,1} with warp factors that are powers of the logarithm of the AdS radius. Thus, our solution encodes a new type of emergent quantum near-criticality. We carry out some stability checks for our solutions. We also set up a consistent ansatz for baryonic black 2-branes of M-theory that are asymptotic to AdS_4 x Q^{1,1,1}.

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arXiv2010

Membranes with Topological Charge and AdS4/CFT3 Correspondence

If the second Betti number b_2 of a Sasaki-Einstein manifold Y^7 does not vanish, then M-theory on AdS_4 x Y^7 possesses "topological" U(1)^{b_2} gauge symmetry. The corresponding Abelian gauge fields come from three-form fluctuations with one index in AdS_4 and the other two in Y^7. We find black membrane solutions carrying one of these U(1) charges. In the zero temperature limit, our solutions interpolate between AdS_4 x Y^7 in the UV and AdS_2 x R^2 x squashed Y^7 in the IR. In fact, the AdS_2 x R^2 x squashed Y^7 background is by itself a solution of the supergravity equations of motion. These solutions do not appear to preserve any supersymmetry. We search for their possible instabilities and do not find any. We also discuss the meaning of our charged membrane backgrounds in a dual quiver Chern-Simons gauge theory with a global U(1) charge density. Finally, we present a simple analytic solution which has the same IR but different UV behavior. We reduce this solution to type IIA string theory, and perform T-duality to type IIB. The type IIB metric turns out to be a product of the squashed Y^7 and the extremal BTZ black hole. We discuss an interpretation of this type IIB background in terms of the (1+1)-dimensional CFT on D3-branes partially wrapped over the squashed Y^7.

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arXiv2010

Compactification Effects in D-brane Inflation

We determine the scalar potential for a D3-brane in a warped conifold background subject to general ultraviolet perturbations. Incorporating the effects of imaginary anti-self-dual (IASD) fluxes and four-dimensional curvature at the nonlinear level, we compute the leading terms in the D3-brane potential. We then provide strong cross-checks of our results by reproducing them in the dual gauge theory. Finally, we observe that the D3-brane potential induced by nonperturbative effects on D7-branes can be represented by a ten-dimensional supergravity solution containing suitable IASD fluxes. Our method allows for the systematic inclusion of compactification effects and serves to constrain the D3-brane effective action in a large class of stabilized compactifications.

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arXiv2010

D3-brane Potentials from Fluxes in AdS/CFT

We give a comprehensive treatment of the scalar potential for a D3-brane in a warped conifold region of a compactification with stabilized moduli. By studying general ultraviolet perturbations in supergravity, we systematically incorporate `compactification effects' sourced by supersymmetry breaking in the compact space. Significant contributions to the D3-brane potential, including the leading term in the infrared, arise from imaginary anti-self-dual (IASD) fluxes. For an arbitrary Calabi-Yau cone, we determine the most general IASD fluxes in terms of scalar harmonics, then compute the resulting D3-brane potential. Specializing to the conifold, we identify the operator dual to each mode of flux, and for chiral operators we confirm that the potential computed in the gauge theory matches the gravity result. The effects of four-dimensional curvature, including the leading D3-brane mass term, arise directly from the ten-dimensional equations of motion. Furthermore, we show that gaugino condensation on D7-branes provides a local source for IASD flux. This flux precisely encodes the nonperturbative contributions to the D3-brane potential, yielding a promising ten-dimensional representation of four-dimensional nonperturbative effects. Our result encompasses all significant contributions to the D3-brane potential discussed in the literature, and does so in the single coherent framework of ten-dimensional supergravity. Moreover, we identify new terms with irrational scaling dimensions that were inaccessible in prior works. By decoupling gravity in a noncompact configuration, then systematically reincorporating compactification effects as ultraviolet perturbations, we have provided an approach in which Planck-suppressed contributions to the D3-brane effective action can be computed.

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arXiv2009

M2-branes and AdS/CFT

These notes provide a brief introduction to the ABJM theory, the level k U(N) x U(N) superconformal Chern-Simons matter theory which has been conjectured to describe N coincident M2-branes. We discuss its dual formulation in terms of M-theory on AdS_4 x S^7/Z_k and review some of the evidence in favor of the conjecture. We end with a brief discussion of the important role played by the monopole operators.

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arXiv2009

Charges of Monopole Operators in Chern-Simons Yang-Mills Theory

We calculate the non-abelian R-charges of BPS monopole operators in three-dimensional gauge theories with N=3 supersymmetry. This class of models includes ABJM theory, the proposed gauge theory dual of M-theory on AdS_4 x S^7/Z_k, as a special case. In the UV limit of the N=3 theories the Yang-Mills coupling becomes weak and the monopole operators are described by classical backgrounds. This allows us to find their SU(2)_R charges in a one-loop computation which by virtue of the non-renormalization of non-abelian R-charges yields the exact result for any value of the coupling. The spectrum of SU(2)_R charges is found by quantizing the SU(2)/U(1) collective coordinate of the BPS background, whose dynamics is that of a charged particle on a sphere with a Wess-Zumino term representing a magnetic monopole at its center. If the Wess-Zumino coefficient is h, then the smallest possible SU(2)_R representation for BPS monopole operators has spin |h|/2. We find, in agreement with earlier proposals, that h is proportional to the sum of the U(1)_R charges of all the fermion fields weighted by the effective monopole charges determined by their gauge representations. The field content of ABJM theory is such that h=0. This proves for any Chern-Simons level k the existence of monopole operators which are singlets under all global symmetries and have vanishing scaling dimensions. These operators are essential for matching the spectrum of the ABJM theory with supergravity and for the supersymmetry enhancement to N=8.

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arXiv2009

M2-branes on Orbifolds of the Cone over Q^{1,1,1}

We study the N=2 supersymmetric Chern-Simons quiver gauge theory recently introduced in arXiv:0809.3237 to describe M2-branes on a cone over the well-known Sasaki-Einstein manifold Q^{1,1,1}. For Chern-Simons levels (k,k,-k,-k) we argue that this theory is dual to AdS_4 x Q^{1,1,1}/Z_k. We derive the Z_k orbifold action and show that it preserves geometrical symmetry U(1)_R x SU(2) x U(1), in agreement with the symmetry of the gauge theory. We analyze the simplest gauge invariant chiral operators, and show that they match Kaluza-Klein harmonics on AdS_4 x Q^{1,1,1}/Z_k. This provides a test of the gauge theory, and in particular of its sextic superpotential which plays an important role in restricting the spectrum of chiral operators. We proceed to study other quiver gauge theories corresponding to more complicated orbifolds of Q^{1,1,1}. In particular, we propose two U(N)^4 Chern-Simons gauge theories whose quiver diagrams are the same as in the 4d theories describing D3-branes on a complex cone over F_0, a Z_2 orbifold of the conifold (in 4d the two quivers are related by the Seiberg duality). The manifest symmetry of these gauge theories is U(1)_R x SU(2) x SU(2). We argue that these gauge theories at levels (k,k,-k,-k) are dual to AdS_4 x Q^{2,2,2}/Z_k. We exhibit calculations of the moduli space and of the chiral operator spectrum which provide support for this conjecture. We also briefly discuss a similar correspondence for AdS_4 x M^{3,2}/Z_k. Finally, we discuss resolutions of the cones and their dual gauge theories.

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arXiv2009

The Squashed, Stretched, and Warped Gets Perturbed

We use direct Kaluza-Klein reduction to calculate the spectrum of spin-2 modes around a warped product of AdS_4 and a certain squashed and stretched 7-sphere. The modes turn out to be polynomials in the four complex variables parameterizing the sphere, and their complex conjugates. The background, which possesses U(1)_R x SU(3) symmetry, has been conjectured to be dual to a U(N) x U(N) N=2 superconformal Chern-Simons theory with a sextic superpotential. We find that the U(1)_R x SU(3) quantum numbers of spin-2 modes are in agreement with those determined in arXiv:0809.3773 through a group theoretic method, and with the spectrum of spin-2 gauge invariant operators in the Chern-Simons gauge theory. The mass-squared in AdS_4 is found to be quadratic in these quantum numbers and the Kaluza-Klein excitation number. Most of the spin-2 operators belong to long multiplets, and we determine their dimensions via the AdS/CFT correspondence.

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arXiv2009

Holographic Systematics of D-brane Inflation

We provide a systematic treatment of possible corrections to the inflaton potential for D-brane inflation in the warped deformed conifold. We consider the D3-brane potential in the presence of the most general possible corrections to the throat geometry sourced by coupling to the bulk of a compact Calabi-Yau space. This corresponds to the potential on the Coulomb branch of the dual gauge theory, in the presence of arbitrary perturbations of the Lagrangian. The leading contributions arise from perturbations by the most relevant operators that do not destroy the throat geometry. We find a generic contribution from a non-chiral operator of dimension $Δ=2$ associated with a global symmetry current, resulting in a negative contribution to the inflaton mass-squared. If the Calabi-Yau preserves certain discrete symmetries, this is the dominant correction to the inflaton potential, and fine-tuning of the inflaton mass is possible. In the absence of such discrete symmetries, the dominant contribution comes from a chiral operator with $Δ=3/2$, corresponding to a $ϕ^{3/2}$ term in the inflaton potential. The resulting inflationary models are phenomenologically similar to the inflection point scenarios arising from specific D7-brane embeddings, but occur under far more general circumstances. Our strategy extends immediately to other warped geometries, given sufficient knowledge of the Kaluza-Klein spectrum.

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arXiv2008

Gauge-String Dualities and Some Applications

The first part of these lectures contains an introductory review of the AdS/CFT duality and of its tests. Applications to thermal gauge theory are also discussed briefly. The second part is devoted to a review of gauge-string dualities based on various warped conifold backgrounds, and to their cosmological applications.

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arXiv2007

On Normal Modes of a Warped Throat

As shown in arXiv:hep-th/0405282, the warped deformed conifold has two bosonic massless modes, a pseudoscalar and a scalar, that are dual to the phase and the modulus of the baryonic condensates in the cascading gauge theory. We reconsider the scalar mode sector, mixing fluctuations of the NS-NS 2-form and the metric, and include non-zero 4-d momentum $k_μ$. The resulting pair of coupled equations produce a discrete spectrum of $m_4^2=- k_μ^2$ which is interpreted as the spectrum of $J^{PC}= 0^{+-}$ glueballs in the gauge theory. Similarly, we derive the spectrum of certain pseudoscalar glueballs with $J^{PC}= 0^{--}$, which originate from the decoupled fluctuations of the RR 2-form. We argue that each of the massive scalar or pseudoscalar modes we find belongs to a 4-d massive axial vector or vector supermultiplet. We also discuss our results in the context of a finite length throat embedded into a type IIB flux compactification.

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arXiv2007

Towards an Explicit Model of D-brane Inflation

We present a detailed analysis of an explicit model of warped D-brane inflation, incorporating the effects of moduli stabilization. We consider the potential for D3-brane motion in a warped conifold background that includes fluxes and holomorphically-embedded D7-branes involved in moduli stabilization. Although the D7-branes significantly modify the inflaton potential, they do not correct the quadratic term in the potential, and hence do not cause a uniform change in the slow-roll parameter eta. Nevertheless, we present a simple example based on the Kuperstein embedding of D7-branes, z_1=constant, in which the potential can be fine-tuned to be sufficiently flat for inflation. To derive this result, it is essential to incorporate the fact that the compactification volume changes slightly as the D3-brane moves. We stress that the compactification geometry dictates certain relationships among the parameters in the inflaton Lagrangian, and these microscopic constraints impose severe restrictions on the space of possible models. We note that the shape of the final inflaton potential differs from projections given in earlier studies: in configurations where inflation occurs, it does so near an inflection point. Finally, we comment on the difficulty of making precise cosmological predictions in this scenario. This is the companion paper to arXiv:0705.3837.

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arXiv2007

Entanglement as a Probe of Confinement

We investigate the entanglement entropy in gravity duals of confining large $N_c$ gauge theories using the proposal of arXiv:hep-th/0603001, arXiv:hep-th/0605073. Dividing one of the directions of space into a line segment of length $l$ and its complement, the entanglement entropy between the two subspaces is given by the classical action of the minimal bulk hypersurface which approaches the endpoints of the line segment at the boundary. We find that in confining backgrounds there are generally two such surfaces. One consists of two disconnected components localized at the endpoints of the line segment. The other contains a tube connecting the two components. The disconnected surface dominates the entropy for $l$ above a certain critical value $l_{\rm crit}$ while the connected one dominates below that value. The change of behavior at $l=l_{\rm crit}$ is reminiscent of the finite temperature deconfinement transition: for $l < l_{\rm crit}$ the entropy scales as $N_c^2$, while for $l > l_{\rm crit}$ as $N_c^0$. We argue that a similar transition should occur in any field theory with a Hagedorn spectrum of non-interacting bound states. The requirement that the entanglement entropy has a phase transition may be useful in constraining gravity duals of confining theories.

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