arXiv subjects

Vijay Balasubramanian

Publications and source records attributed to Vijay Balasubramanian.

At least 109 records · Page 6Linked to original sources

arXiv2013

A strongly coupled zig-zag transition

The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Previous studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of velocities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an experimentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the large central charge limit of the CFT. The model has a rich phase structure with new qualitative features, already in the two Majorana fermion case. The AdS/CFT calculation involves considering back reaction in space-time to capture subleading effects.

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arXiv2013

The Sense of Place: Grid Cells in the Brain and the Transcendental Number e

Grid cells in the brain respond when an animal occupies a periodic lattice of "grid fields" during spatial navigation. The grid scale varies along the dorso-ventral axis of the entorhinal cortex. We propose that the grid system minimizes the number of neurons required to encode location with a given resolution. We derive several predictions that match recent experiments: (i) grid scales follow a geometric progression, (ii) the ratio between adjacent grid scales is the square root of e for idealized neurons, and robustly lies in the range 1.4-1.7 for realistic neurons, (iii) the scale ratio varies modestly within and between animals, (iv) the ratio between grid scale and individual grid field widths at that scale also lies in this range, (v) grid fields lie on a triangular lattice. The theory also predicts the optimal grids in one and three dimensions, and the total number of discrete scales.

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arXiv2012

Holographic interpretations of the renormalization group

In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the bulk fields fluctuate. Recent work has used a Wilsonian framework to propose an alternative identification of the running couplings in terms of non-fluctuating data; in the classical limit, these new couplings do not satisfy the bulk equations of motion. We study renormalization scheme dependence in the latter formalism, and show that a scheme exists in which couplings to single trace operators realize particular solutions to the bulk equations of motion, in the semiclassical limit. This occurs for operators with dimension $Δ\notin \frac{d}{2} + \ZZ$, for sufficiently low momenta. We then clarify the relation between the saddle point approximation to the Wilsonian effective action ($S_W$) and boundary conditions at a cutoff surface in AdS space. In particular, we interpret non-local multi-trace operators in $S_W$ as arising in Lorentzian AdS space from the temporary passage of excitations through the UV region that has been integrated out. Coarse-graining these operators makes the action effectively local.

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arXiv2012

Global embeddings for branes at toric singularities

We describe how local toric singularities, including the Toric Lego construction, can be embedded in compact Calabi-Yau manifolds. We study in detail the addition of D-branes, including non-compact flavor branes as typically used in semi-realistic model building. The global geometry provides constraints on allowable local models. As an illustration of our discussion we focus on D3 and D7-branes on (the partially resolved) (dP0)^3 singularity, its embedding in a specific Calabi-Yau manifold as a hypersurface in a toric variety, the related type IIB orientifold compactification, as well as the corresponding F-theory uplift. Our techniques generalize naturally to complete intersections, and to a large class of F-theory backgrounds with singularities.

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arXiv2011

Momentum-space entanglement and renormalization in quantum field theory

The degrees of freedom of any interacting quantum field theory are entangled in momentum space. Thus, in the vacuum state, the infrared degrees of freedom are described by a density matrix with an entanglement entropy. We derive a relation between this density matrix and the conventional Wilsonian effective action. We argue that the entanglement entropy of and mutual information between subsets of field theoretic degrees of freedom at different momentum scales are natural observables in quantum field theory and demonstrate how to compute these in perturbation theory. The results may be understood heuristically based on the scale-dependence of the coupling strength and number of degrees of freedom. We measure the rate at which entanglement between degrees of freedom declines as their scales separate and suggest that this decay is related to the property of decoupling in quantum field theory.

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arXiv2011

Vacuum decay in multidimensional field landscapes: thin, thick and intersecting walls

We study tunneling between vacua in multi-dimensional field spaces. Working in the strict thin wall approximation, we find that the conventional instantons for false vacuum decay develop a new vanishing eigenvalue in their fluctuation determinant, arising from decorations of the nucleating bubble wall with small spots of the additional vacua. Naively, this would suggest that the presence of additional vacua in field space leads to a substantial enhancement of the nucleation rate. However, we argue that this potential enhancement is regulated away by the finite thickness of physical bubble wall intersections. We then discuss novel saddle points of the thin wall action that, in some regimes of parameter space, have the potential to destabilize the conventional instantons for false vacuum decay.

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arXiv2011

What we don't know about time

String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.

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arXiv2011

Holographic Thermalization

Using the AdS/CFT correspondence, we probe the scale-dependence of thermalization in strongly coupled field theories following a quench, via calculations of two-point functions, Wilson loops and entanglement entropy in d=2,3,4. In the saddlepoint approximation these probes are computed in AdS space in terms of invariant geometric objects - geodesics, minimal surfaces and minimal volumes. Our calculations for two-dimensional field theories are analytical. In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent non-analyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first. For homogeneous initial conditions the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound over the range of scales studied. The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes.

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arXiv2011

Quantitative approaches to information recovery from black holes

The evaporation of black holes into apparently thermal radiation poses a serious conundrum for theoretical physics: at face value, it appears that in the presence of a black hole quantum evolution is non-unitary and destroys information. This information loss paradox has its seed in the presence of a horizon causally separating the interior and asymptotic regions in a black hole spacetime. A quantitative resolution of the paradox could take several forms: (a) a precise argument that the underlying quantum theory is unitary, and that information loss must be an artifact of approximations in the derivation of black hole evaporation, (b) an explicit construction showing how information can be recovered by the asymptotic observer, (c) a demonstration that the causal disconnection of the black hole interior from infinity is an artifact of the semiclassical approximation. This review summarizes progress on all these fronts.

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arXiv2011

Natural images from the birthplace of the human eye

Here we introduce a database of calibrated natural images publicly available through an easy-to-use web interface. Using a Nikon D70 digital SLR camera, we acquired about 5000 six-megapixel images of Okavango Delta of Botswana, a tropical savanna habitat similar to where the human eye is thought to have evolved. Some sequences of images were captured unsystematically while following a baboon troop, while others were designed to vary a single parameter such as aperture, object distance, time of day or position on the horizon. Images are available in the raw RGB format and in grayscale. Images are also available in units relevant to the physiology of human cone photoreceptors, where pixel values represent the expected number of photoisomerizations per second for cones sensitive to long (L), medium (M) and short (S) wavelengths. This database is distributed under a Creative Commons Attribution-Noncommercial Unported license to facilitate research in computer vision, psychophysics of perception, and visual neuroscience.

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arXiv2010

Helical Luttinger Liquids and Three Dimensional Black Holes

Cold interacting fermions in two dimensions form exactly solvable Luttinger liquids, whose characteristic scaling exponents differ from those of conventional Fermi liquids. We use the AdS/CFT correspondence to discuss an equivalence between a class of helical, strongly coupled Luttinger liquids and fermions propagating in the background of a 3D black hole. The microscopic Lagrangian is explicitly known and the construction is fully embeddable in string theory. The retarded Green function at low temperature and energy arises from the geometry very near the black hole horizon. This structure is universal for all cold, charged liquids with a dual description in gravity.

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arXiv2010

States of a chiral 2d CFT

We study the dual description of the self-dual orbifold, a locally AdS_3 spacetime which is a circle fibration over AdS_2 and arises as the near-horizon limit of the extreme BTZ black hole. The geometry has two boundaries; we argue that this should correspond to a saddle-point for two copies of a chiral CFT living on these two boundaries in an entangled state. This picture arises naturally in the near-horizon limit, but there is a potential inconsistency with the bulk physics because of causal connections between the boundaries. We discuss a possible resolution of this puzzle. We also construct geometries which asymptotically approach the self-dual orbifold on a single boundary. These geometries (which contain mild singularities) enable us to explore other states of the dual chiral CFT. One of the geometries corresponds to the ground state of this CFT and can be obtained as a particular near-horizon limit of the BTZ M=0 black hole. The self-dual orbifold is a finite temperature version of this geometry.

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arXiv2010

Fast, scalable, Bayesian spike identification for multi-electrode arrays

We present an algorithm to identify individual neural spikes observed on high-density multi-electrode arrays (MEAs). Our method can distinguish large numbers of distinct neural units, even when spikes overlap, and accounts for intrinsic variability of spikes from each unit. As MEAs grow larger, it is important to find spike-identification methods that are scalable, that is, the computational cost of spike fitting should scale well with the number of units observed. Our algorithm accomplishes this goal, and is fast, because it exploits the spatial locality of each unit and the basic biophysics of extracellular signal propagation. Human intervention is minimized and streamlined via a graphical interface. We illustrate our method on data from a mammalian retina preparation and document its performance on simulated data consisting of spikes added to experimentally measured background noise. The algorithm is highly accurate.

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arXiv2009

What is a chiral 2d CFT? And what does it have to do with extremal black holes?

The near horizon limit of the extremal BTZ black hole is a``self-dual orbifold'' of AdS_3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS_2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS_2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS_2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.

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arXiv2009

Toric Lego: A method for modular model building

Within the context of local type IIB models arising from branes at toric Calabi-Yau singularities, we present a systematic way of joining any number of desired sectors into a consistent theory. The different sectors interact via massive messengers with masses controlled by tunable parameters. We apply this method to a toy model of the minimal supersymmetric standard model (MSSM) interacting via gauge mediation with a metastable supersymmetry breaking sector and an interacting dark matter sector. We discuss how a mirror procedure can be applied in the type IIA case, allowing us to join certain intersecting brane configurations through massive mediators.

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arXiv2009

Quantum geometry and gravitational entropy

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.

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arXiv2008

Quiver Topology and RG Dynamics

Renormalization group flows of quiver gauge theories play a central role in determining the low-energy properties of string vacua. We demonstrate that useful predictions about the RG dynamics of a quiver gauge theory may be extracted from the global structure of its quiver diagram. For quiver theories of a certain type, we develop an efficient and practical method for determining which superpotential deformations generate a flow to an interacting conformal fixed point.

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arXiv2008

Black Holes as Effective Geometries

Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective theory. By studying examples in M-theory on AdS_3 x S^2 x CY that preserve 4 supersymmetries we show how this can happen.

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