Arvind Murugan

Entanglement as a probe of confinement

Abstract We investigate the entanglement entropy in gravity duals of confining large N c gauge theories using the proposal of [S. Ryu, T. Takayanagi, Phys. Rev. Lett. 96 (2006) 181602, hep-th/0603001 ; S. Ryu, T. Takayanagi, JHEP 0608 (2006) 045, 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 crit while the connected one dominates below that value. The change of behavior at l = l crit is reminiscent of the finite temperature deconfinement transition: for l l crit the entropy scales as N c 2 , while for l > l 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.

On D3-brane potentials in compactifications with fluxes and wrapped D-branes

We study the potential governing D3-brane motion in a warped throat region of a string compactification with internal fluxes and wrapped D-branes. If the Kahler moduli of the compact space are stabilized by nonperturbative effects, a D3-brane experiences a force due to its interaction with D-branes wrapping certain four-cycles. We compute this interaction, as a correction to the warped four-cycle volume, using explicit throat backgrounds in supergravity. This amounts to a closed-string channel computation of the loop corrections to the nonperturbative superpotential that stabilizes the volume. We demonstrate that for warped conical spaces the superpotential correction is given by the embedding equation specifying the wrapped four-cycle, in agreement with the general form proposed by Ganor. We verify that the corrected gauge coupling on wrapped D7-branes is holomorphic. Finally, our results have applications to cosmological inflation models in which the inflaton corresponds to a D3-brane moving in a warped throat.

Gauge/gravity duality and warped resolved conifold

We study supergravity backgrounds encoded through the gauge/string correspondence by the SU(N) × SU(N) theory arising on N D3-branes on the conifold. As discussed in hep-th/9905104, the dynamics of this theory describes warped versions of both the singular and the resolved conifolds through different (symmetry breaking) vacua. We construct these supergravity solutions explicitly and match them with the gauge theory with different sets of vacuum expectation values of the bi-fundamental fields A1,A2,B1,B2. For the resolved conifold, we find a non-singular SU(2) × U(1) × U(1) symmetric warped solution produced by a stack of D3-branes localized at a point on the blown-up 2-sphere. It describes a smooth RG flow from AdS5 × T1,1 in the UV to AdS5 × S5 in the IR, produced by giving a VEV to just one field, e.g. B2. The presence of a condensate of baryonic operator detB2 is confirmed using a Euclidean D3-brane wrapping a 4-cycle inside the resolved conifold. The Greens functions on the singular and resolved conifolds are central to our calculations and are discussed in some detail.

AdS4/CFT3 squashed, stretched and warped

We use group theoretic methods to calculate the spectrum of short multiplets around the extremum of = 8 gauged supergravity potential which possesses = 2 supersymmetry and SU(3) global symmetry. Upon uplifting to M-theory, it describes a warped product of AdS4 and a certain squashed and stretched 7-sphere. We find quantum numbers in agreement with those of the gauge invariant operators in the = 2 superconformal Chern-Simons theory recently proposed to be the dual of this M-theory background. This theory is obtained from the U(N) × U(N) theory through deforming the superpotential by a term quadratic in one of the superfields. To construct this model explicitly, one needs to employ monopole operators whose complete understanding is still lacking. However, for the U(2) × U(2) gauge theory we make a proposal for the form of the monopole operators which has a number of desired properties. In particular, this proposal implies enhanced symmetry of the U(2) × U(2) ABJM theory for k = 1,2; it makes its similarity to and subtle difference from the BLG theory quite explicit.

Speed, dissipation, and error in kinetic proofreading

Proofreading mechanisms increase specificity in biochemical reactions by allowing for the dissociation of intermediate complexes. These mechanisms disrupt and reset the reaction to undo errors at the cost of increased time of reaction and free energy expenditure. Here, we draw an analogy between proofreading and microtubule growth which share some of the features described above. Our analogy relates the statistics of growth and shrinkage of microtubules in physical space to the cycling of intermediate complexes in the space of chemical states in proofreading mechanisms. Using this analogy, we find a new kinetic regime of proofreading in which an exponential speed-up of the process can be achieved at the cost of a somewhat larger error rate. This regime is analogous to the transition region between two known growth regimes of microtubules (bounded and unbounded) and is sharply defined in the limit of large proofreading networks. We find that this advantageous regime of speed-error tradeoff might be present in proofreading schemes studied earlier in the charging of tRNA by tRNA synthetases, in RecA filament assembly on ssDNA, and in protein synthesis by ribosomes.

Goldstone Bosons and Global Strings in a Warped Resolved Conifold

A warped resolved conifold background of type IIB theory, constructed in hep-th/0701064, is dual to the supersymmetric SU(N) × SU(N) gauge theory with a vacuum expectation value (VEV) for one of the bifundamental chiral superfields. This VEV breaks both the superconformal invariance and the baryonic symmetry. The absolute value of the VEV controls the resolution parameter of the conifold. In this paper we study the phase of the VEV, which corresponds to the Goldstone boson of the broken symmetry. We explicitly construct the linearized perturbation of the 4-form R-R potential that contains the Goldstone boson. On general grounds, the theory should contain global strings which create a monodromy of the pseudoscalar Goldstone boson field. We identify these strings with the D3-branes wrapping the two-cycle at the tip of the warped resolved conifold.

Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures

Significance Self-assembly has recently emerged as a powerful technique for synthesizing structures on the nano- and microscales. The basis of this development is the use of biopolymers, like DNA, to design specific interactions between multiple species of components, allowing the spontaneous assembly of complex structures. Our work addresses a fundamental limitation of the existing approaches to self-assembly: Namely, every target structure must have its own dedicated set of components, which are programmed to assemble only that very structure. In contrast, in biological systems, the same set of components can assemble many different complexes. Inspired by this, we extend the self-assembly framework to mixtures of shared components capable of assembling distinct structures on demand. Self-assembly materials are traditionally designed so that molecular or mesoscale components form a single kind of large structure. Here, we propose a scheme to create “multifarious assembly mixtures,” which self-assemble many different large structures from a set of shared components. We show that the number of multifarious structures stored in the solution of components increases rapidly with the number of different types of components. However, each stored structure can be retrieved by tuning only a few parameters, the number of which is only weakly dependent on the size of the assembled structure. Implications for artificial and biological self-assembly are discussed.

Information capacity of specific interactions

Significance The past 15 years have seen a proliferation of experimental techniques aimed at engineering self-assembled structures. These bottom–up techniques rely on specific interactions between components that arise from diverse physical mechanisms such as chemical affinities and shape complementarity attraction. Comparisons of specificity across such diverse systems, each with unique physics and constraints, can be difficult. Here we describe an information theoretic measure, capacity, to quantify specificity in a range of recent experimental systems. Capacity quantifies the maximal amount of information that can be encoded and then resolved by a system of specific interactions, as a function of experimentally tunable parameters. Our framework can be applied to specific interactions of diverse origins, from colloidal experiments to protein interactions. Specific interactions are a hallmark feature of self-assembly and signal-processing systems in both synthetic and biological settings. Specificity between components may arise from a wide variety of physical and chemical mechanisms in diverse contexts, from DNA hybridization to shape-sensitive depletion interactions. Despite this diversity, all systems that rely on interaction specificity operate under the constraint that increasing the number of distinct components inevitably increases off-target binding. Here we introduce “capacity,” the maximal information encodable using specific interactions, to compare specificity across diverse experimental systems and to compute how specificity changes with physical parameters. Using this framework, we find that “shape” coding of interactions has higher capacity than chemical (“color”) coding because the strength of off-target binding is strongly sublinear in binding-site size for shapes while being linear for colors. We also find that different specificity mechanisms, such as shape and color, can be combined in a synergistic manner, giving a capacity greater than the sum of the parts.

Topologically protected modes in non-equilibrium stochastic systems

Non-equilibrium driving of biophysical processes is believed to enable their robust functioning despite the presence of thermal fluctuations and other sources of disorder. Such robust functions include sensory adaptation, enhanced enzymatic specificity and maintenance of coherent oscillations. Elucidating the relation between energy consumption and organization remains an important and open question in non-equilibrium statistical mechanics. Here we report that steady states of systems with non-equilibrium fluxes can support topologically protected boundary modes that resemble similar modes in electronic and mechanical systems. Akin to their electronic and mechanical counterparts, topological-protected boundary steady states in non-equilibrium systems are robust and are largely insensitive to local perturbations. We argue that our work provides a framework for how biophysical systems can use non-equilibrium driving to achieve robust function.

Receptor arrays optimized for natural odor statistics.

Significance Natural odors typically consist of many molecules at different concentrations, which together determine the odor identity. This information is collectively encoded by olfactory receptors and then forwarded to the brain. However, it is unclear how the receptor activity can encode both the composition of the odor and the concentrations of its constituents. We study a simple model of the olfactory receptors from which we derive design principles for optimally communicating odor information in a given natural environment. We use these results to discuss biological olfactory systems, and we propose how they can be used to improve artificial sensor arrays. Natural odors typically consist of many molecules at different concentrations. It is unclear how the numerous odorant molecules and their possible mixtures are discriminated by relatively few olfactory receptors. Using an information theoretic model, we show that a receptor array is optimal for this task if it achieves two possibly conflicting goals: (i) Each receptor should respond to half of all odors and (ii) the response of different receptors should be uncorrelated when averaged over odors presented with natural statistics. We use these design principles to predict statistics of the affinities between receptors and odorant molecules for a broad class of odor statistics. We also show that optimal receptor arrays can be tuned to either resolve concentrations well or distinguish mixtures reliably. Finally, we use our results to predict properties of experimentally measured receptor arrays. Our work can thus be used to better understand natural olfaction, and it also suggests ways to improve artificial sensor arrays.