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Bulk local states and crosscaps in holographic CFT

In a weakly coupled gravity theory in the anti-de Sitter space, local states in the bulk are linear superpositions of Ishibashi states for a crosscap in the dual conformal field theory. The superposition structure can be constrained either by the microscopic causality in the bulk gravity or the bootstrap condition in the boundary conformal field theory. We show, contrary to some...

Bulk locality and boundary creating operators

Physics and Mathematics of the Universe, University of Tokyo 3 and Hirosi Ooguri 4 Open Access , c The Authors 5 5-1-5 Kashiwanoha , Kashiwa, Chiba 277-8583 , Japan We formulate a minimum requirement for

Shortening anomalies in supersymmetric theories

We present new anomalies in two-dimensional \( \mathcal{N}=\left(2,2\right) \) superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background superfields in short representations. Therefore, standard results that follow from \( \mathcal{N}=\left(2...

Reflections on conformal spectra

We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions Δ0 of external operators. We use these symmetries to motivate...

Gravitational positive energy theorems from information inequalities

In this paper we argue that classical asymptotically anti-de Sitter spacetimes that arise as states in consistent ultraviolet completions of Einstein gravity coupled to matter must satisfy an infinite family of positive energy conditions. To each ball-shaped spatial region BB of the boundary spacetime we can associate a bulk spatial region ΣBΣB between BB and the bulk extremal...

The holographic entropy cone

We initiate a systematic enumeration and classification of entropy inequalities satisfied by the Ryu-Takayanagi formula for conformal field theory states with smooth holographic dual geometries. For 2, 3, and 4 regions, we prove that the strong subadditivity and the monogamy of mutual information give the complete set of inequalities. This is in contrast to the situation for...

Wall Crossing as Seen by Matrix Models

The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are naturally related to the Kähler moduli space \({{\mathcal M}(X)}\) . We construct unitary one-matrix models which count such BPS states for a class of...

Schwinger-Dyson Equation in Three-Dimensional Simplicial Quantum Gravity

We study the simplicial quantum gravity in three dimensions. Motivated by Boulatov's model which generates a sum over simplicial complexes weighted with the Turaev-Viro invariant, we introduce boundary operators in the simplicial gravity associated to compact orientable surfaces. An amplitude of the boundary operator is given by a sum over triangulations in the interior of the...

One-Loop Effective Potential in Anti-de Sitter Space

A scheme is given to compute the one-loop effective potential in a general class of curved spacetime which are homogeneous and globally static. The renormalized effective potential for scalar field theories in anti-de Sitter background is evaluated by this method. The computation based on the Sp background is disproved by demonstrating that this prescription does not respect the...

Gauge Invariant Local Action of String Field from BRS Formalism

A systematic prescription is given to find the “original” gauge-invariant string field Lagrangian from Siegel’s gauge-fixed Lagrangian containing an infinite tower of ghosts’ ghosts. A local and gauge-invariant Lagrangian of free bosonic string field is constructed in a complete form by this method. It reproduces Neveu and West’s result up to the sixth excited level order. We...