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Open Access Publications from the University of California

Scholarly Works (6 results)

  • Article
  • Peer Reviewed
UC Santa Barbara Previously Published Works (2016)
We study entanglement in states of holographic CFTs defined by Euclidean path integrals over geometries with slowly varying metrics. In particular, our CFT spacetimes have $S^1$ fibers whose size $b$ varies along one direction ($x$) of an ${\mathbb R}^{d-1}$ base. Such examples respect an ${\mathbb R}^{d-2}$ Euclidean symmetry. Treating the $S^1$ direction as time leads to a thermofield double state on a spacetime with adiabatically varying redshift, while treating another direction as time leads to a confining ground state with slowly varying confinement scale. In both contexts the entropy of slab-shaped regions defined by $|x - x_0| \le L$ exhibits well-known phase transitions at length scales $L= L_{crit}$ characterizing the CFT entanglements. For the thermofield double, the numerical coefficients governing the effect of variations in $b(x)$ on the transition are surprisingly small and exhibit an interesting change of sign: gradients reduce $L_{crit}$ for $d \le 3$ but increase $L_{crit}$ for $d\ge4$. This means that, while for general $L > L_{crit}$ they significantly increase the mutual information of opposing slabs as one would expect, for $d\ge 4$ gradients cause a small decrease near the phase transition. In contrast, for the confining ground states gradients always decrease $L_{crit}$, with the effect becoming more pronounced in higher dimensions.
    Cover page: Adiabatic corrections to holographic entanglement in thermofield doubles and confining ground states
    • Article
    • Peer Reviewed
    UC Santa Barbara Previously Published Works (2018)
    We consider the non-local operator ${\mathcal T}$ defined in 2-dimensional CFTs by the path integral over a torus with two punctures. Using the AdS/CFT correspondence, we study the spectrum and ground state of this operator in holographic such CFTs in the limit of large central charge $c$. In one region of moduli space, we argue that the operator retains a finite gap and has a ground state that differs from the CFT vacuum only by order one corrections. In this region the torus operator is much like the cylinder operator. But in another region of moduli space we find a puzzle. Although our ${\mathcal T}$ is of the manifestly positive form $A^\dagger A$, studying the most tractable phases of $\text{Tr}( {\mathcal T}^n)$ suggests that ${\mathcal T}$ has negative eigenvalues. It seems clear that additional phases must become relevant at large $n$, perhaps leading to novel behavior associated with a radically different ground state or a much higher density of states. By studying the action of two such torus operators on the CFT ground state, we also provide evidence that, even at large $n$, the relevant bulk saddles have $t=0$ surfaces with small genus.
      Cover page: The torus operator in holography
      • Article
      • Peer Reviewed
      UC Santa Barbara Previously Published Works (2016)
      As noted by Witten, compactifying a $d$-dimensional holographic CFT on an $S^1$ gives a class of $(d-1)$-dimensional confining theories with gravity duals. The prototypical bulk solution dual to the ground state is a double Wick rotation of the AdS$_{d+1}$ Schwarzschild black hole known as the AdS soliton. We generalize such examples by allowing slow variations in the size of the $S^1$, and thus in the confinement scale. Coefficients governing the second order response of the system are computed for $3 \le d \le 8$ using a derivative expansion closely related to the fluid-gravity correspondence. The primary physical results are that i) gauge-theory flux tubes tend to align orthogonal to gradients and along the eigenvector of the Hessian with the lowest eigenvalue, ii) flux tubes aligned orthogonal to gradients are attracted to gradients for $d \le 6$ but repelled by gradients for $d \ge 7$, iii) flux tubes are repelled by regions where the second derivative along the tube is large and positive but are attracted to regions where the eigenvalues of the Hessian are large and positive in directions orthogonal to the tube, and iv) for $d > 3$, inhomogeneities act to raise the total energy of the confining vacuum above its zeroth order value.
        Cover page: Holographic confinement in inhomogeneous backgrounds
        • Thesis
        • Peer Reviewed
        UC Santa Barbara Electronic Theses and Dissertations (2017)

        This dissertation focuses on the role classical black hole spacetimes play in the AdS/CFT correspondence. We begin by introducing some of the puzzles surrounding black holes, and we review their connection to strongly correlated CFT states through holography. Additionally, we detail numerical methods for constructing black hole states of non-trivial topology in three dimensions and evaluating their actions.

        In part I we focus on using black hole spacetimes to derive insights into holography and quantum gravity. Using numerical methods, we study a class of non-local operators in the CFT, defined via a path integral over a torus with two punctures. In particular, we are interested in determining the spectrum of such operators at various points in moduli space. In the dual gravitational theory, such an operator might be used to construct black hole spacetimes with arbitrarily high topology behind the horizon. We present evidence suggesting this fails, and along the way encounter a puzzle related to the positivity of these operators. The resolution of this puzzle lies in developing technology to better catalogue the relevant gravitational phases.

        Additionally, we use multi-boundary wormhole spacetimes to investigate the constraints on the subregion entanglement entropies of holographic states. We find tension with previously claimed properties of these constraints, namely that they define a polyhedral cone in the space of entanglement entropies. These results either suggest the possible existence of further unknown constraints, or the need for a more complicated construction procedure to realize the extremal states.

        In part II we focus on the holographic description of CFT states via black hole spacetimes, focusing on spacetimes perturbatively constructed from the planar AdS-Schwarzschild metric. First, we consider corrections to properties of confining ground states of holographic CFTs as we introduce spatial curvature. Next, we compute shifts in vacuum entanglement entropy in a thermal state with a locally varying temperature as well as similar shifts in the confining ground states with spatial curvature.

        • 3 supplemental files
        Cover page: Black Holes and Holography: Insights and Applications
        • Article
        • Peer Reviewed
        UC Santa Barbara Previously Published Works (2017)
        The notion of a holographic entropy cone has recently been introduced and it has been proven that this cone is polyhedral. However, the original definition was fully geometric and did not strictly require a holographic duality. We introduce a new definition of the cone, insisting that the geometries used for its construction should be dual to states of a CFT. As a result, the polyhedrality of this holographic cone does not immediately follow. A numerical evaluation of the Euclidean action for the geometries that realize extremal rays of the original cone indicates that these are subdominant bulk phases of natural path integrals. The result challenges the expectation that such geometries are in fact dual to CFT states.
          Cover page: Handlebody phases and the polyhedrality of the holographic entropy cone
          • Article
          • Peer Reviewed
          UC Santa Barbara Previously Published Works (2017)
          We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the (greedy) entanglement wedge, and where these central elements can also be reconstructed from complementary boundary regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the $\frac{\delta \text{Area}}{4G_N}$ term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this $\frac{\delta \text{Area}}{4G_N}$ term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.
            Cover page: Living on the edge: a toy model for holographic reconstruction of algebras with centers
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