Pure spinor formalism and gauge/string duality

A worldsheet interpretation of AdS/CFT duality from the point of view of a topological open/closed string duality using the power of pure spinor formalism will be studied. We will show that the pure spinor superstring on some maximally supersymmetric backgrounds which admit a particular Z4 automorphism can be recasted as a topological A-model action on a fermionic coset plus a BRST exact term. This topological model will be interpreted as the superstring theory at zero radius. Using this decomposition we will prove the exactness of the \ube-model on these backgrounds. We then show that corresponding to this topological model, there exist a gauged linear sigma model which makes it possible to sketch the superstring theory in the small radius limit as the dual limit of the perturbative gauge theory. Studying the branch geometry of this gauged sigma model in di\uaeerent phases gives information about how the gauge/string duality is realized at small radius from a similar point of view of the topological open/closed conifold duality studied by Gopakumar, Ooguri and Vafa. Moreover, we will discuss possible D-brane boundary conditions in this model. Using this D-branes, we will make an exact check in the N = 4 SYM/AdS5 \ua3 S5 duality. We will show that the exact computation of the expectation value of the circular Wilson loops in the gauge theory side can be obtained from the amplitudes of some particular D-branes as the dual of the Wilson loops in the superstring side. The next step will be to construct a BV action for G=G principal chiral model with G 2 PSU(2; 2j4), we will show that after applying different gauge \uafxings of the model, we will get either a topological A-model theory or a topological thery whose supersymmetric charge is equal to the pure spinor BRST charge. Using this model one can explore the cohomology of the pure spinor action from the topological BV model. Then we show that there exist a particular consistent deformation of the G=G action equal to the pure spinor superstring action. In this way we generate the superstring action on a non-zero radius AdS background as a perturbation around a topological model corresponding to zero radius limit of the superstring theory. Using this picture we will give an argument based on the worldsheet interpretation of open/closed duality to give a worldsheet explanation for AdS/CFT duality. A better understanding of this picture might give a prove of Maldacena's conjecture. At the end we will show that using the topological A-model, one can also give a prescription for computing multiloop amplitudes in the superstring theory on AdS5 \ua3 S5 background

Exploring Pure Spinor String Theory on AdS_4 x CP^3

In this paper we formulate the pure spinor superstring theory on AdS_4 x CP^3. By recasting the pure spinor action as a topological A-model on the fermionic supercoset Osp(6|4)/SO(6)xSp(4) plus a BRST exact term, we prove the exactness of the sigma-model. We then give a gauged linear sigma-model which reduces to the superstring in the limit of large volume and we study its branch geometry in different phases. Moreover, we discuss possible D-brane boundary conditions and the principal chiral model for the fermionic supercoset.Comment: 26 pages, typos corrected, references adde

Rhythmic auditory cortex activity at multiple timescales shapes stimulus–response gain and background firing

The phase of low-frequency network activity in the auditory cortex captures changes in neural excitability, entrains to the temporal structure of natural sounds, and correlates with the perceptual performance in acoustic tasks. Although these observations suggest a causal link between network rhythms and perception, it remains unknown how precisely they affect the processes by which neural populations encode sounds. We addressed this question by analyzing neural responses in the auditory cortex of anesthetized rats using stimulus–response models. These models included a parametric dependence on the phase of local field potential rhythms in both stimulus-unrelated background activity and the stimulus–response transfer function. We found that phase-dependent models better reproduced the observed responses than static models, during both stimulation with a series of natural sounds and epochs of silence. This was attributable to two factors: (1) phase-dependent variations in background firing (most prominent for delta; 1–4 Hz); and (2) modulations of response gain that rhythmically amplify and attenuate the responses at specific phases of the rhythm (prominent for frequencies between 2 and 12 Hz). These results provide a quantitative characterization of how slow auditory cortical rhythms shape sound encoding and suggest a differential contribution of network activity at different timescales. In addition, they highlight a putative mechanism that may implement the selective amplification of appropriately timed sound tokens relative to the phase of rhythmic auditory cortex activity

Implications of the Dependence of Neuronal Activity on Neural Network States for the Design of Brain-Machine Interfaces.

Brain-machine interfaces (BMIs) can improve the quality of life of patients with sensory and motor disabilities by both decoding motor intentions expressed by neural activity, and by encoding artificially sensed information into patterns of neural activity elicited by causal interventions on the neural tissue. Yet, current BMIs can exchange relatively small amounts of information with the brain. This problem has proved difficult to overcome by simply increasing the number of recording or stimulating electrodes, because trial-to-trial variability of neural activity partly arises from intrinsic factors (collectively known as the network state) that include ongoing spontaneous activity and neuromodulation, and so is shared among neurons. Here we review recent progress in characterizing the state dependence of neural responses, and in particular of how neural responses depend on endogenous slow fluctuations of network excitability. We then elaborate on how this knowledge may be used to increase the amount of information that BMIs exchange with brain. Knowledge of network state can be used to fine-tune the stimulation pattern that should reliably elicit a target neural response used to encode information in the brain, and to discount part of the trial-by-trial variability of neural responses, so that they can be decoded more accurately

State-Dependent Decoding Algorithms Improve the Performance of a Bidirectional BMI in Anesthetized Rats.

Brain-machine interfaces (BMIs) promise to improve the quality of life of patients suffering from sensory and motor disabilities by creating a direct communication channel between the brain and the external world. Yet, their performance is currently limited by the relatively small amount of information that can be decoded from neural activity recorded form the brain. We have recently proposed that such decoding performance may be improved when using state-dependent decoding algorithms that predict and discount the large component of the trial-to-trial variability of neural activity which is due to the dependence of neural responses on the network's current internal state. Here we tested this idea by using a bidirectional BMI to investigate the gain in performance arising from using a state-dependent decoding algorithm. This BMI, implemented in anesthetized rats, controlled the movement of a dynamical system using neural activity decoded from motor cortex and fed back to the brain the dynamical system's position by electrically microstimulating somatosensory cortex. We found that using state-dependent algorithms that tracked the dynamics of ongoing activity led to an increase in the amount of information extracted form neural activity by 22%, with a consequently increase in all of the indices measuring the BMI's performance in controlling the dynamical system. This suggests that state-dependent decoding algorithms may be used to enhance BMIs at moderate computational cost

On gauge/string correspondence and mirror symmetry

We consider a mirror dual of the Berkovits-Vafa A-model for the BPS superstring on $AdS_5\times S^5$ in the form of a deformed superconifold. Via geometric transition, the theory has a dual description as the hermitian gaussian one-matrix model. We show that the A-model amplitudes of generic $AdS_2\times S^4$ branes, breaking the superconformal symmetry as $U(2,2|4)\to OSp(4^*|4)$, are evaluated in terms of observables in the matrix model. As such, upon the usual identification $g_{YM}^2=g_s$, these can be expanded as Drukker-Gross circular 1/2-BPS Wilson loops in the perturbative regime of ${\cal N}=4$ SYM.Comment: 1+13 pages, minor changes, added refrences, version to appear in JHE

The structures and functions of correlations in neural population codes

The collective activity of a population of neurons, beyond the properties of individual cells, is crucial for many brain functions. A fundamental question is how activity correlations between neurons affect how neural populations process information. Over the past 30 years, major progress has been made on how the levels and structures of correlations shape the encoding of information in population codes. Correlations influence population coding through the organization of pairwise-activity correlations with respect to the similarity of tuning of individual neurons, by their stimulus modulation and by the presence of higher-order correlations. Recent work has shown that correlations also profoundly shape other important functions performed by neural populations, including generating codes across multiple timescales and facilitating information transmission to, and readout by, downstream brain areas to guide behaviour. Here, we review this recent work and discuss how the structures of correlations can have opposite effects on the different functions of neural populations, thus creating trade-offs and constraints for the structure-function relationships of population codes. Further, we present ideas on how to combine large-scale simultaneous recordings of neural populations, computational models, analyses of behaviour, optogenetics and anatomy to unravel how the structures of correlations might be optimized to serve multiple functions