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Register a new userConductivity bounds in probe brane models
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We discuss upper and lower bounds on the electrical conductivity of finite temperature strongly coupled quantum field theories, holographically dual to probe brane models, within linear response. In a probe limit where disorder is introduced entirely through an inhomogeneous background charge density, we find simple lower and upper bounds on the electrical conductivity in arbitrary dimensions. In field theories in two spatial dimensions, we show that both bounds persist even when disorder is included in the bulk metric. We discuss the challenges with finding sharp lower bounds on conductivity in three or more spatial dimensions when the metric is inhomogeneous.
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We compute the exact density of states and 2-point function of the $mathcal{N} =2$ super-symmetric SYK model in the large $N$ double-scaled limit, by using combinatorial tools that relate the moments of the distribution to sums over oriented chord diagrams. In particular we show how SUSY is realized on the (highly degenerate) Hilbert space of chords. We further calculate analytically the number of ground states of the model in each charge sector at finite $N$, and compare it to the results from the double-scaled limit. Our results reduce to the super-Schwarzian action in the low energy short interaction length limit. They imply that the conformal ansatz of the 2-point function is inconsistent due to the large number of ground states, and we show how to add this contribution. We also discuss the relation of the model to $SL_q(2|1)$. For completeness we present an overview of the $mathcal{N}=1$ super-symmetric SYK model in the large $N$ double-scaled limit.
The concepts of operator size and computational complexity play important roles in the study of quantum chaos and holographic duality because they help characterize the structure of time-evolving Heisenberg operators. It is particularly important to understand how these microscopically defined measures of complexity are related to notions of complexity defined in terms of a dual holographic geometry, such as complexity-volume (CV) duality. Here we study partially entangled thermal states in the Sachdev-Ye-Kitaev (SYK) model and their dual description in terms of operators inserted in the interior of a black hole in Jackiw-Teitelboim (JT) gravity. We compare a microscopic definition of complexity in the SYK model known as K-complexity to calculations using CV duality in JT gravity and find that both quantities show an exponential-to-linear growth behavior. We also calculate the growth of operator size under time evolution and find connections between size and complexity. While the notion of operator size saturates at the scrambling time, our study suggests that complexity, which is well defined in both quantum systems and gravity theories, can serve as a useful measure of operator evolution at both early and late times.
We propose a charged falling particle in an AdS space as a holographic model of local charged quench generalizing model of arXiv:1302.5703. The quench is followed by evolving currents and inhomogeneous distribution of chemical potential. We derive the analytical formula describing the evolution of the entanglement entropy. At some characteristic time after the quench, we find that the entanglement shows a sharp dip. This effect is universal and independent of the dimension of the system. At finite temperature generalization of this model, we find that multiple dips and ramps appear.
We use numerical bootstrap techniques to study correlation functions of scalars transforming in the adjoint representation of $SU(N)$ in three dimensions. We obtain upper bounds on operator dimensions for various representations and study their dependence on $N$. We discover new families of kinks, one of which could be related to bosonic QED${}_3$. We then specialize to the cases $N=3,4$, which have been conjectured to describe a phase transition respectively in the ferromagnetic complex projective model $CP^2$ and the antiferromagnetic complex projective model $ACP^{3}$. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to small regions overlapping with the lattice predictions.
We investigate a weak version of subsystem eigenstate thermalization hypothesis (ETH) for a two-dimensional large central charge conformal field theory by comparing the local equivalence of high energy state and thermal state of canonical ensemble. We evaluate the single-interval Renyi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of Renyi entropy by two different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central charge expansion. We then evaluate the relative entropy of the reduced density matrices to measure the difference between the heavy primary state and thermal state of canonical ensemble, and find that the aforementioned nontrivial eighth order results make the relative entropy unsuppressed in the large central charge limit. By using Pinskers and Fannes-Audenaert inequalities, we can exploit the results of relative entropy to yield the lower and upper bounds on trace distance of the excited-state and thermal-state reduced density matrices. Our results are consistent with subsystem weak ETH, which requires the above trace distance is of power-law suppression by the large central charge. However, we are unable to pin down the exponent of power-law suppression. As a byproduct we also calculate the relative entropy to measure the difference between the reduced density matrices of two different heavy primary states.
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