arXiv subjects

Shamit Kachru

Publications and source records attributed to Shamit Kachru.

At least 55 records · Page 3Linked to original sources

arXiv2015

Elliptic Genera and 3d Gravity

We describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of $K3$, product manifolds, certain simple families of Calabi-Yau hypersurfaces, and symmetric products of the "Monster CFT." We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions we attempt to quantify the fraction of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.

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arXiv2015

Exceptional Algebra and Sporadic Groups at c=12

In earlier works, it was seen that a ${\mathbb Z}/2$ orbifold of the theory of 24 free two-dimensional chiral fermions admits various sporadic finite simple groups as global symmetry groups when viewed as an ${\cal N}=1$, ${\cal N}=2$, or ${\cal N}=4$ superconformal field theory. In this note, we show that viewing the same theory as an SCFT with extended ${\cal N}=1$ symmetry -- where the extension is the same one which arises in string compactification on manifolds of exceptional Spin$(7)$ holonomy -- yields theories which have global symmetry given by the sporadic groups $M_{24}, Co_2$ or $Co_3$. The partition functions twined by these symmetries, when decomposed into characters of the Spin(7) algebra, give rise to two-component vector-valued mock modular forms encoding an infinite-dimensional module for the corresponding sporadic groups.

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arXiv2015

Enhanced Pairing of Quantum Critical Metals Near d=3+1

We study the dynamics of a quantum critical boson coupled to a Fermi surface in intermediate energy regimes where the Landau damping of the boson can be parametrically controlled, either via large Fermi velocity or by large N techniques. We focus on developing a systematic approach to studying the BCS instability, including careful treatment of the enhanced log^2 and log^3 singularities which appear already at 1-loop. We also treat possible instabilities to charge density wave (CDW) formation, and compare the scales Lambda_{BCS} and Lambda_{CDW} of the onset of the instabilities in different parametric regimes. We address the question of whether the dressing of the fermions into a non-Fermi liquid via interactions with the order parameter field can happen at energies > Lambda_{BCS}, Lambda_{CDW}.

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arXiv2014

Emergent Fermi surfaces, fractionalization and duality in supersymmetric QED

We study the physics of 3d supersymmetric abelian gauge theories (with small supersymmetry breaking perturbations) at finite density. Using mirror symmetry, which provides a natural generalization of the duality between the XY model and the abelian Higgs model but now including fermionic fields, we see many dynamical phenomena conjectured to be of relevance in condensed matter systems. In particular, we find examples of the emergence of a Fermi surface at low energies from hybridization of fermions localized at magnetic defects at high energies, as well as fractionalization of charged fermions into spinon-holon pairs with the concomitant appearance of emergent gauge fields. We also find dual descriptions for Fermi surfaces coupled to critical bosons, which give rise to non-Fermi liquids.

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arXiv2014

Slow Fermions in Quantum Critical Metals

We study the low-energy behavior of metals coupled to gapless bosons. This problem arises in several contexts in modern condensed matter physics; we focus on the theory of metals near continuous quantum phase transitions (where the boson is the order parameter). In the vicinity of d=3 spatial dimensions, the upper critical dimension of the theory, the ratio of fermion and boson speeds, v/c, acts as an additional control parameter, enabling us to access IR fixed points where this ratio vanishes. This limit corresponds to a non-Fermi liquid coupled to bosons with critical exponents governed by the Wilson-Fisher fixed point.

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arXiv2014

Interpolating from Bianchi Attractors to Lifshitz and AdS Spacetimes

We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or $AdS_2 \times S^3$ geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or $AdS_2 \times S^3$ geometries can in turn be connected to $AdS_5$ spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to $AdS_5$ spacetime. The asymptotic $AdS_5$ spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points.

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arXiv2014

A Simple Harmonic Universe

We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. In the case of moderate bounces (where the ratio of the maximal scale factor $a_+$ to the minimal scale factor $a_-$ is ${\cal O}(1)$), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large $a_+/a_-$, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.

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arXiv2013

Non-Fermi liquid behavior of large N_B quantum critical metals

The problem of continuous quantum phase transitions in metals involves critical bosons coupled to a Fermi surface. We solve the theory in the limit of a large number, N_B, of bosonic flavors, where the bosons transform in the adjoint representation, while the fermions are in the fundamental representation of a global SU(N_B) flavor symmetry group. The leading large N_B solution corresponds to a non-Fermi liquid coupled to Wilson-Fisher bosons. In a certain energy range, the fermion velocity vanishes - resulting in the destruction of the Fermi surface. Subleading 1/N_B corrections correspond to a qualitatively different form of Landau damping of the bosonic critical fluctuations. We discuss the model in d=3-epsilon but because of the additional control afforded by large N_B, our results are valid down to d=2. In the limit epsilon << 1, the large N_B solution is consistent with the RG analysis of Ref. 1.

cond-mat.str-el↗

arXiv2013

Mathieu Moonshine and N=2 String Compactifications

There is a `Mathieu moonshine' relating the elliptic genus of K3 to the sporadic group M_{24}. Here, we give evidence that this moonshine extends to part of the web of dualities connecting heterotic strings compactified on K3 \times T^2 to type IIA strings compactified on Calabi-Yau threefolds. We demonstrate that dimensions of M_{24} representations govern the new supersymmetric index of the heterotic compactifications, and appear in the Gromov--Witten invariants of the dual Calabi-Yau threefolds, which are elliptic fibrations over the Hirzebruch surfaces F_n.

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arXiv2013

Non-Fermi liquid fixed point in a Wilsonian theory of quantum critical metals

We study the problem of disorder-free metals near a continuous quantum critical point. We depart from the standard paradigm of Hertz and Millis, and treat both fermions and bosons i.e. order parameter fields) on equal footing. We construct a Wilsonian effective field theory that integrates out only high energy boson and fermion modes. Below the upper critical dimension of the theory (d=3 spatial dimensions), we find new fixed points in which the bosons are described by the Wilson-Fisher fixed point and are coupled to a non-Fermi liquid metal. We describe subtleties with the renormalization group flow of four-Fermi interactions, which can be surmounted in a controlled large N limit. In this limit, we find that the theory has no superconducting instability.

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arXiv2013

Twining Genera of (0,4) Supersymmetric Sigma Models on K3

Conformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E8xE8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E8xE8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera - elliptic genera with appropriate insertions of discrete symmetry generators in the trace - for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M24.

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arXiv2013

Supersymmetric Defect Models and Mirror Symmetry

We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d N=4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d N=2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of N=4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.

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arXiv2013

Vortex Lattices and Crystalline Geometries

We consider $AdS_2 \times R^2$ solutions supported by a magnetic field, such as those which arise in the near-horizon limit of magnetically charged $AdS_4$ Reissner-Nordstrom black branes. In the presence of an electrically charged scalar field, such magnetic solutions can be unstable to spontaneous formation of a vortex lattice. We solve the coupled partial differential equations which govern the charged scalar, gauge field, and metric degrees of freedom to lowest non-trivial order in an expansion around the critical point, and discuss the corrections to the free energy and thermodynamic functions arising from the formation of the lattice. We describe how such solutions can also be interpreted, via S-duality, as characterizing infrared crystalline phases of conformal field theories doped by a chemical potential, but in zero magnetic field; the doped conformal field theories are dual to geometries that exhibit dynamical scaling and hyperscaling violation.

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arXiv2013

Extremal Horizons with Reduced Symmetry: Hyperscaling Violation, Stripes, and a Classification for the Homogeneous Case

Classifying the zero-temperature ground states of quantum field theories with finite charge density is a very interesting problem. Via holography, this problem is mapped to the classification of extremal charged black brane geometries with anti-de Sitter asymptotics. In a recent paper [1], we proposed a Bianchi classification of the extremal near-horizon geometries in five dimensions, in the case where they are homogeneous but, in general, anisotropic. Here, we extend our study in two directions: we show that Bianchi attractors can lead to new phases, and generalize the classification of homogeneous phases in a way suggested by holography. In the first direction, we show that hyperscaling violation can naturally be incorporated into the Bianchi horizons. We also find analytical examples of "striped" horizons. In the second direction, we propose a more complete classification of homogeneous horizon geometries where the natural mathematics involves real four-algebras with three dimensional sub-algebras. This gives rise to a richer set of possible near-horizon geometries, where the holographic radial direction is non-trivially intertwined with field theory spatial coordinates. We find examples of several of the new types in systems consisting of reasonably simple matter sectors coupled to gravity, while arguing that others are forbidden by the Null Energy Condition. Extremal horizons in four dimensions governed by three-algebras or four-algebras are also discussed.

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arXiv2012

Bianchi Attractors: A Classification of Extremal Black Brane Geometries

Extremal black branes are of interest because they correspond to the ground states of field theories at finite charge density in gauge/gravity duality. The geometry of such a brane need not be translationally invariant in the spatial directions along which it extends. A less restrictive requirement is that of homogeneity, which still allows points along the spatial directions to be related to each other by symmetries. In this paper, we find large new classes of homogeneous but anisotropic extremal black brane horizons, which could naturally arise in gauge/gravity dual pairs. In 4+1 dimensional spacetime, we show that such homogeneous black brane solutions are classified by the Bianchi classification, which is well known in the study of cosmology, and fall into nine classes. In a system of Einstein gravity with negative cosmological term coupled to one or two massive Abelian gauge fields, we find solutions with an additional scaling symmetry, which could correspond to the near-horizon geometries of such extremal black branes. These solutions realize many of the Bianchi classes. In one case, we construct the complete extremal solution which asymptotes to AdS space.

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arXiv2012

A New Theory of Anyons

We study a 2+1 dimensional theory of bosons and fermions with an omega ~ k^2 dispersion relation. The most general interactions consistent with specific symmetries impart fractional statistics to the fermions. Unlike examples involving Chern-Simons gauge theories, our statistical phases derive from the exchange of gapless propagating bosons with marginal interactions. Even though no gap exists, we show that the anyonic statistics are precisely defined. Symmetries combine with the vacuum structure to guarantee the non-renormalization of our anyonic phases.

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arXiv2012

Aspects of holography for theories with hyperscaling violation

We analyze various aspects of the recently proposed holographic theories with general dynamical critical exponent z and hyperscaling violation exponent $θ$. We first find the basic constraints on $z, θ$ from the gravity side, and compute the stress-energy tensor expectation values and scalar two-point functions. Massive correlators exhibit a nontrivial exponential behavior at long distances, controlled by $θ$. At short distance, the two-point functions become power-law, with a universal form for $θ> 0$. Next, the calculation of the holographic entanglement entropy reveals the existence of novel phases which violate the area law. The entropy in these phases has a behavior that interpolates between that of a Fermi surface and that exhibited by systems with extensive entanglement entropy. Finally, we describe microscopic embeddings of some $θ\neq 0$ metrics into full string theory models -- these metrics characterize large regions of the parameter space of Dp-brane metrics for $p\neq 3$. For instance, the theory of N D2-branes in IIA supergravity has z=1 and $θ= -1/3$ over a wide range of scales, at large $g_s N$.

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arXiv2012

Resolving Lifshitz Horizons

Via the AdS/CFT correspondence, ground states of field theories at finite charge density are mapped to extremal black brane solutions. Studies of simple gravity + matter systems in this context have uncovered wide new classes of extremal geometries. The Lifshitz metrics characterising field theories with non-trivial dynamical critical exponent $z \neq 1$ emerge as one common endpoint in doped holographic toy models. However, the Lifshitz horizon exhibits mildly singular behaviour - while curvature invariants are finite, there are diverging tidal forces. Here we show that in some of the simplest contexts where Lifshitz metrics emerge, Einstein-Maxwell-dilaton theories, generic corrections lead to a replacement of the Lifshitz metric, in the deep infrared, by a re-emergent $AdS_2 \times R^2$ geometry. Thus, at least in these cases, the Lifshitz scaling characterises the physics over a wide range of energy scales, but the mild singularity is cured by quantum or stringy effects.

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