arXiv subjects

Vijay Balasubramanian

Publications and source records attributed to Vijay Balasubramanian.

At least 73 records · Page 4Linked to original sources

arXiv2020

Knitting Wormholes by Entanglement in Supergravity

We construct a single-boundary wormhole geometry in type IIB supergravity by perturbing two stacks of $N$ extremal D3-branes in the decoupling limit. The solution interpolates from a two-sided planar AdS-Schwarzschild geometry in the interior, through a harmonic two-center solution in the intermediate region, to an asymptotic AdS space. The construction involves a CPT twist in the gluing of the wormhole to the exterior throats that gives a global monodromy to some coordinates, while preserving orientability. The geometry has a dual interpretation in $\mathcal{N}=4$ $SU(2N)$ Super Yang-Mills theory in terms of a Higgsed $SU(2N) \to S(U(N) \times U(N))$ theory in which $\mathcal{O} (N^2)$ degrees of freedom in each $SU(N)$ sector are entangled in an approximate thermofield double state at a temperature much colder than the Higgs scale. We argue that the solution can be made long-lived by appropriate choice of parameters, and comment on mechanisms for generating traversability. We also describe a construction of a double wormhole between two universes.

hep-th↗

arXiv2020

Efficient coding of natural scene statistics predicts discrimination thresholds for grayscale textures

Previously, in (Hermundstad et al., 2014), we showed that when sampling is limiting, the efficient coding principle leads to a "variance is salience" hypothesis, and that this hypothesis accounts for visual sensitivity to binary image statistics. Here, using extensive new psychophysical data and image analysis, we show that this hypothesis accounts for visual sensitivity to a large set of grayscale image statistics at a striking level of detail, and also identify the limits of the prediction. We define a 66-dimensional space of local grayscale light-intensity correlations, and measure the relevance of each direction to natural scenes. The "variance is salience" hypothesis predicts that two-point correlations are most salient, and predicts their relative salience. We tested these predictions in a texture-segregation task using un-natural, synthetic textures. As predicted, correlations beyond second order are not salient, and predicted thresholds for over 300 second-order correlations match psychophysical thresholds closely (median fractional error <0.13).

q-bio.NC↗

arXiv2020

Spin structures and baby universes

We extend a 2d topological model of the gravitational path integral to include sums over spin structure, corresponding to Neveu-Schwarz (NS) or Ramond (R) boundary conditions for fermions. The Euclidean path integral vanishes when the number of R boundaries is odd. This path integral corresponds to a correlator of boundary creation operators on a non-trivial baby universe Hilbert space. The non-factorization necessitates a dual interpretation of the bulk path integral in terms of a product of partition functions (associated to NS boundaries) and Witten indices (associated to R boundaries), averaged over an ensemble of theories with varying Hilbert space dimension and different numbers of bosonic and fermionic states. We also consider a model with End-of-the-World (EOW) branes: the dual ensemble then includes a sum over randomly chosen fermionic and bosonic states. We propose two modifications of the bulk path integral which restore an interpretation in a single dual theory: (i) a geometric prescription where we add extra boundaries with a sum over their spin structures, and (ii) an algebraic prescription involving "spacetime D-branes". We extend our ideas to Jackiw-Teitelboim gravity, and propose a dual description of a single unitary theory with spin structure in a system with eigenbranes.

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arXiv2020

Quantum Complexity of Time Evolution with Chaotic Hamiltonians

We study the quantum complexity of time evolution in large-$N$ chaotic systems, with the SYK model as our main example. This complexity is expected to increase linearly for exponential time prior to saturating at its maximum value, and is related to the length of minimal geodesics on the manifold of unitary operators that act on Hilbert space. Using the Euler-Arnold formalism, we demonstrate that there is always a geodesic between the identity and the time evolution operator $e^{-iHt}$ whose length grows linearly with time. This geodesic is minimal until there is an obstruction to its minimality, after which it can fail to be a minimum either locally or globally. We identify a criterion - the Eigenstate Complexity Hypothesis (ECH) - which bounds the overlap between off-diagonal energy eigenstate projectors and the $k$-local operators of the theory, and use it to show that the linear geodesic will at least be a local minimum for exponential time. We show numerically that the large-$N$ SYK model (which is chaotic) satisfies ECH and thus has no local obstructions to linear growth of complexity for exponential time, as expected from holographic duality. In contrast, we also study the case with $N=2$ fermions (which is integrable) and find short-time linear complexity growth followed by oscillations. Our analysis relates complexity to familiar properties of physical theories like their spectra and the structure of energy eigenstates and has implications for the hypothesized computational complexity class separations PSPACE $\nsubseteq$ BQP/poly and PSPACE $\nsubseteq$ BQSUBEXP/subexp, and the "fast-forwarding" of quantum Hamiltonians.

hep-th↗

arXiv2020

Holographic Probes of Inner Horizons

We study the inner horizons of rotating and charged black holes in anti-de Sitter space. These black holes have a classical analytic extension through the inner horizon to additional asymptotic regions. If this extension survives in the quantum theory, it requires particular analytic properties in a dual CFT, which give a prescription for calculating correlation functions for operators placed on any asymptotic boundary of the maximally extended spacetime. We show that for charged black holes in three or greater dimensions, and rotating black holes in four or greater dimensions, these analytic properties are inconsistent in the dual CFT, implying the absence of an analytic extension for quantum fields past the inner horizon. Thus, we find that strong cosmic censorship holds for all AdS black holes except rotating BTZ. To further study the latter case, we insert classical perturbations near the boundary at late times, producing shockwaves traveling along the inner horizon. We holographically compute CFT correlators in this background that probe a high energy scattering process near the inner horizon and argue that the shockwave does not destabilize the inner horizon violently enough to prevent signaling between different asymptotic regions of the Penrose diagram. This provides evidence that the rotating BTZ black hole does violate the strong cosmic censorship conjecture.

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arXiv2020

Geometric secret sharing in a model of Hawking radiation

We consider a black hole in three dimensional AdS space entangled with an auxiliary radiation system. We model the microstates of the black hole in terms of a field theory living on an end of the world brane behind the horizon, and allow this field theory to itself have a holographic dual geometry. This geometry is also a black hole since entanglement of the microstates with the radiation leaves them in a mixed state. This "inception black hole" can be purified by entanglement through a wormhole with an auxiliary system which is naturally identified with the external radiation, giving a realization of the ER=EPR scenario. In this context, we propose an extension of the Ryu-Takayanagi (RT) formula, in which extremal surfaces computing entanglement entropy are allowed to pass through the brane into its dual geometry. This new rule reproduces the Page curve for evaporating black holes, consistently with the recently proposed "island formula". We then separate the radiation system into pieces. Our extended RT rule shows that the entanglement wedge of the union of radiation subsystems covers the black hole interior at late times, but the union of entanglement wedges of the subsystems may not. This result points to a secret sharing scheme in Hawking radiation wherein reconstruction of certain regions in the interior is impossible with any subsystem of the radiation, but possible with all of it.

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arXiv2020

Superluminal chaos after a quantum quench

Thermal states holographically dual to black holes in Einstein gravity display maximal Lyapunov growth as well as "butterfly effect cones". We study these effects in highly non-equilibrium states, obtained from an initial thermal state by the sudden injection of energy. We do this by computing out-of-time-order correlators (OTOCs) in BTZ-Vaidya spacetimes, which describe transitions between black holes at different temperatures. If both pairs of boundary operators appearing in the OTOC are inserted before the energy injection, we recover standard results, with butterfly effect cones displaying a light-cone structure. But when one pair of operators is inserted before and the other pair after the energy injection, the Lyapunov growth saturates the chaos bounds set by the local temperatures and the butterfly effect cones "open up", becoming superluminal, albeit in a way that does not violate causality. In the limiting case, in which the initial state is the vacuum, Lyapunov growth only starts after the energy injection. Our computations of the OTOCs are phrased in terms of gravitationally interacting particles, where fields are treated in a geodesic approximation and the eikonal phase shift is expressed in terms of stress tensors and shock waves associated to geodesics.

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arXiv2019

A geometric attractor mechanism for self-organization of entorhinal grid modules

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of "grid fields" in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated by ratios in the range 1.2--2.0. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

q-bio.NC↗

arXiv2019

The size of the immune repertoire of bacteria

Some bacteria and archaea possess an immune system, based on the CRISPR-Cas mechanism, that confers adaptive immunity against phage. In such species, individual bacteria maintain a "cassette" of viral DNA elements called spacers as a memory of past infections. The typical cassette contains a few dozen spacers. Given that bacteria can have very large genomes, and since having more spacers should confer a better memory, it is puzzling that so little genetic space would be devoted by bacteria to their adaptive immune system. Here, we identify a fundamental trade-off between the size of the bacterial immune repertoire and effectiveness of response to a given threat, and show how this tradeoff imposes a limit on the optimal size of the CRISPR cassette.

q-bio.PE↗

arXiv2019

A competitive binding model predicts nonlinear responses of olfactory receptors to complex mixtures

In color vision, the quantitative rules for mixing lights to make a target color are well understood. By contrast, the rules for mixing odorants to make a target odor remain elusive. A solution to this problem in vision relied on characterizing receptor responses to different wavelengths of light and subsequently relating these responses to perception. In olfaction, experimentally measuring receptor responses to a representative set of complex mixtures is intractable due to the vast number of possibilities. To meet this challenge, we develop a biophysical model that predicts mammalian receptor responses to complex mixtures using responses to single odorants. The dominant nonlinearity in our model is competitive binding (CB): only one odorant molecule can attach to a receptor binding site at a time. This simple framework predicts receptor responses to mixtures of up to twelve monomolecular odorants to within 15\% of experimental observations and provides a powerful method for leveraging limited experimental data. Simple extensions of our model describe phenomena such as synergy, overshadowing, and inhibition. We demonstrate that the presence of such interactions can be identified via systematic deviations from the competitive binding model.

q-bio.NC↗

arXiv2019

Entanglement versus entwinement in symmetric product orbifolds

We study the entanglement entropy of gauged internal degrees of freedom in a two dimensional symmetric product orbifold CFT, whose configurations consist of $N$ strands sewn together into "long" strings, with wavefunctions symmetrized under permutations. In earlier work a related notion of "entwinement" was introduced. Here we treat this system analogously to a system of $N$ identical particles. From an algebraic point of view, we point out that the reduced density matrix on $k$ out of $N$ particles is not associated with a subalgebra of operators, but rather with a linear subspace, which we explain is sufficient. In the orbifold CFT, we compute the entropy of a single strand in states holographically dual in the D1/D5 system to a conical defect geometry or a massless BTZ black hole and find a result identical to entwinement. We also calculate the entropy of two strands in the state that represents the conical defect; the result differs from entwinement. In this case, matching entwinement would require finding a gauge-invariant way to impose continuity across strands.

hep-th↗

arXiv2019

Information flows in strongly coupled ABJM theory

We use holographic methods to characterize the RG flow of quantum information in a Chern-Simons theory coupled to massive fermions. First, we use entanglement entropy and mutual information between strips to derive the dimension of the RG-driving operator and a monotonic c-function. We then display a scaling regime where, unlike in a CFT, the mutual information between strips changes non-monotonically with strip width, vanishing in both IR and UV but rising to a maximum at intermediate scales. The associated information transitions also contribute to non-monotonicity in the conditional mutual information which characterizes the independence of neighboring strips after conditioning on a third. Finally, we construct a measure of extensivity which tests to what extent information that region A shares with regions B and C is additive. In general, mutual information is super-extensive in holographic theories, and we might expect super-extensivity to be maximized in CFTs since they are scale-free. Surprisingly, our massive theory is more super-extensive than a CFT in a range of scales near the UV limit, although it is less super-extensive than a CFT at all lower scales. Our analysis requires the full ten-dimensional dual gravity background, and the extremal surfaces computing entanglement entropy explore all of these dimensions.

hep-th↗

arXiv2019

Adaptation of olfactory receptor abundances for efficient coding

Olfactory receptor usage is highly heterogeneous, with some receptor types being orders of magnitude more abundant than others. We propose an explanation for this striking fact: the receptor distribution is tuned to maximally represent information about the olfactory environment in a regime of efficient coding that is sensitive to the global context of correlated sensor responses. This model predicts that in mammals, where olfactory sensory neurons are replaced regularly, receptor abundances should continuously adapt to odor statistics. Experimentally, increased exposure to odorants leads variously, but reproducibly, to increased, decreased, or unchanged abundances of different activated receptors. We demonstrate that this diversity of effects is required for efficient coding when sensors are broadly correlated, and provide an algorithm for predicting which olfactory receptors should increase or decrease in abundance following specific environmental changes. Finally, we give simple dynamical rules for neural birth and death processes that might underlie this adaptation.

q-bio.NC↗

arXiv2018

The dual of non-extremal area: differential entropy in higher dimensions

The Ryu-Takayanagi formula relates entanglement entropy in a field theory to the area of extremal surfaces anchored to the boundary of a dual AdS space. It is interesting to ask if there is also an information theoretic interpretation of the areas of non-extremal surfaces that are not necessarily boundary-anchored. In general, the physics outside such surfaces is associated to observers restricted to a time-strip in the dual boundary field theory. When the latter is two-dimensional, it is known that the differential entropy associated to the strip computes the length of the dual bulk curve, and has an interpretation in terms of the information cost in Bell pairs of restoring correlations inaccessible to observers in the strip. A general realization of this formalism in higher dimensions is unknown. We first prove a no-go theorem eliminating candidate expressions for higher dimensional differential entropy based on entropic c-theorems. Then we propose a new formula in terms of an integral of shape derivatives of the entanglement entropy of ball shaped regions. Our proposal stems from the physical requirement that differential entropy must be locally finite and conformally invariant. Demanding cancellation of the well-known UV divergences of entanglement entropy in field theory guides us to our conjecture, which we test for surfaces in $AdS_4$. Our results suggest a candidate c-function for field theories in arbitrary dimensions.

hep-th↗

arXiv2018

How a well-adapting immune system remembers

An adaptive agent predicting the future state of an environment must weigh trust in new observations against prior experiences. In this light, we propose a view of the adaptive immune system as a dynamic Bayesian machinery that updates its memory repertoire by balancing evidence from new pathogen encounters against past experience of infection to predict and prepare for future threats. This framework links the observed initial rapid increase of the memory pool early in life followed by a mid-life plateau to the ease of learning salient features of sparse environments. We also derive a modulated memory pool update rule in agreement with current vaccine response experiments. Our results suggest that pathogenic environments are sparse and that memory repertoires significantly decrease infection costs even with moderate sampling. The predicted optimal update scheme maps onto commonly considered competitive dynamics for antigen receptors.

q-bio.PE↗

arXiv2018

Binding Complexity and Multiparty Entanglement

We introduce "binding complexity", a new notion of circuit complexity which quantifies the difficulty of distributing entanglement among multiple parties, each consisting of many local degrees of freedom. We define binding complexity of a given state as the minimal number of quantum gates that must act between parties to prepare it. To illustrate the new notion we compute it in a toy model for a scalar field theory, using certain multiparty entangled states which are analogous to configurations that are known in AdS/CFT to correspond to multiboundary wormholes. Pursuing this analogy, we show that our states can be prepared by the Euclidean path integral in $(0+1)$-dimensional quantum mechanics on graphs with wormhole-like structure. We compute the binding complexity of our states by adapting the Euler-Arnold approach to Nielsen's geometrization of gate counting, and find a scaling with entropy that resembles a result for the interior volume of holographic multiboundary wormholes. We also compute the binding complexity of general coherent states in perturbation theory, and show that for "double-trace deformations" of the Hamiltonian the effects resemble expansion of a wormhole interior in holographic theories.

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arXiv2018

Emergent classical spacetime from microstates of an incipient black hole

Black holes have an enormous underlying space of microstates, but universal macroscopic physics characterized by mass, charge and angular momentum as well as a causally disconnected interior. This leads two related puzzles: (1) How does the effective factorization of interior and exterior degrees of freedom emerge in gravity?, and (2) How does the underlying degeneracy of states wind up having a geometric realization in the horizon area and in properties of the singularity? We explore these puzzles in the context of an incipient black hole in the AdS/CFT correspondence, the microstates of which are dual to half-BPS states of the $\mathcal{N}=4$ super-Yang-Mills theory. First, we construct a code subspace for this black hole and show how to organize it as a tensor product of a universal macroscopic piece (describing the exterior), and a factor corresponding to the microscopic degrees of freedom (describing the interior). We then study the classical phase space and symplectic form for low-energy excitations around the black hole. On the AdS side, we find that the symplectic form has a new physical degree of freedom at the stretched horizon of the black hole, reminiscent of soft hair, which is absent in the microstates. We explicitly show how such a soft mode emerges from the microscopic phase space in the dual CFT via a canonical transformation and how it encodes partial information about the microscopic degrees of freedom of the black hole.

hep-th↗

arXiv2018

Dynamic self-organized error-correction of grid cells by border cells

Grid cells in the entorhinal cortex are believed to establish their regular, spatially correlated firing patterns by path integration of the animal's motion. Mechanisms for path integration, e.g. in attractor network models, predict stochastic drift of grid responses, which is not observed experimentally. We demonstrate a biologically plausible mechanism of dynamic self-organization by which border cells, which fire at environmental boundaries, can correct such drift in grid cells. In our model, experience-dependent Hebbian plasticity during exploration allows border cells to learn connectivity to grid cells. Border cells in this learned network reset the phase of drifting grids. This error-correction mechanism is robust to environmental shape and complexity, including enclosures with interior barriers, and makes distinctive predictions for environmental deformation experiments. Our work demonstrates how diverse cell types in the entorhinal cortex could interact dynamically and adaptively to achieve robust path integration.

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