Generalizing previous results for
We study
This result implies, in particular, that if
 Award ID(s):
 2014215
 NSFPAR ID:
 10477530
 Publisher / Repository:
 Journal of High Energy Physics
 Date Published:
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2023
 Issue:
 6
 ISSN:
 10298479
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

A<sc>bstract</sc> = 0 and$$ \mathcal{N} $$ $N$ = 1, we analyze$$ \mathcal{N} $$ $N$ = 2 JT supergravity on asymptotically AdS_{2}spaces with arbitrary topology and show that this theory of gravity is dual, in a holographic sense, to a certain random matrix ensemble in which supermultiplets of different$$ \mathcal{N} $$ $N$R charge are statistically independent and each is described by its own = 2 random matrix ensemble. We also analyze the case with a timereversal symmetry, either commuting or anticommuting with the$$ \mathcal{N} $$ $N$R charge. In order to compare supergravity to random matrix theory, we develop an = 2 analog of the recursion relations for WeilPetersson volumes originally discovered by Mirzakhani in the bosonic case.$$ \mathcal{N} $$ $N$ 
A<sc>bstract</sc> Euclidean path integrals for UVcompletions of
d dimensional bulk quantum gravity were recently studied in [1] by assuming that they satisfy axioms of finiteness, reality, continuity, reflectionpositivity, and factorization. Sectors of the resulting Hilbert space were then defined for any ($$ {\mathcal{H}}_{\mathcal{B}} $$ ${H}_{B}$d − 2)dimensional surface , where$$ \mathcal{B} $$ $B$ may be thought of as the boundary ∂Σ of a bulk Cauchy surface in a corresponding Lorentzian description, and where$$ \mathcal{B} $$ $B$ includes the specification of appropriate boundary conditions for bulk fields. Cases where$$ \mathcal{B} $$ $B$ was the disjoint union$$ \mathcal{B} $$ $B$B ⊔B of two identical (d − 2)dimensional surfacesB were studied in detail and, after the inclusion of finitedimensional ‘hidden sectors,’ were shown to provide a Hilbert space interpretation of the associated RyuTakayanagi entropy. The analysis was performed by constructing typeI von Neumann algebras ,$$ {\mathcal{A}}_L^B $$ ${A}_{L}^{B}$ that act respectively at the left and right copy of$$ {\mathcal{A}}_R^B $$ ${A}_{R}^{B}$B inB ⊔B .Below, we consider the case of general
, and in particular for$$ \mathcal{B} $$ $B$ =$$ \mathcal{B} $$ $B$B _{L}⊔B _{R}withB _{L},B _{R}distinct. For anyB _{R}, we find that the von Neumann algebra atB _{L}acting on the offdiagonal Hilbert space sector is a central projection of the corresponding typeI von Neumann algebra on the ‘diagonal’ Hilbert space$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$ ${H}_{{B}_{L}\bigsqcup {B}_{R}}$ . As a result, the von Neumann algebras$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$ ${H}_{{B}_{L}\bigsqcup {B}_{L}}$ ,$$ {\mathcal{A}}_L^{B_L} $$ ${A}_{L}^{{B}_{L}}$ defined in [1] using the diagonal Hilbert space$$ {\mathcal{A}}_R^{B_L} $$ ${A}_{R}^{{B}_{L}}$ turn out to coincide precisely with the analogous algebras defined using the full Hilbert space of the theory (including all sectors$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$ ${H}_{{B}_{L}\bigsqcup {B}_{L}}$ ). A second implication is that, for any$$ {\mathcal{H}}_{\mathcal{B}} $$ ${H}_{B}$ , including the same hidden sectors as in the diagonal case again provides a Hilbert space interpretation of the RyuTakayanagi entropy. We also show the above central projections to satisfy consistency conditions that lead to a universal central algebra relevant to all choices of$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$ ${H}_{{B}_{L}\bigsqcup {B}_{R}}$B _{L}andB _{R}. 
A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)
A<sc>bstract</sc> The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higherdimensional antide Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one ignores normalizations, of positive operators. On the CFT side of the correspondence, any two positive operators
A, B will satisfy the trace inequality Tr(AB ) ≤ Tr(A )Tr(B ). This relation holds on any Hilbert space and is deeply associated with the fact that the algebra$$ \mathcal{H} $$ $H$B ( ) of bounded operators on$$ \mathcal{H} $$ $H$ is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate below. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semiclassical expansion and with arbitrary higherderivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for JackiwTeitelboim gravity and we also motivate it for more general theories.$$ \mathcal{H} $$ $H$ 
A<sc>bstract</sc> We introduce Ward identities for superamplitudes in
D dimensional extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for an$$ \mathcal{N} $$ $N$n partice superamplitude take a simple universal form for half BPS and nonBPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of then superparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on halfBPS or nonBPS superfields, given by (D − 2)L + 2 − or ($$ \mathcal{N} $$ $N$D − 2)L + 2 − , respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.$$ 2\mathcal{N} $$ $2N$ 
A<sc>bstract</sc> In this paper we discuss gauging noninvertible zeroform symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form
for$$ \textrm{Rep}\left(\mathcal{H}\right) $$ $\mathrm{Rep}\left(H\right)$ a suitable Hopf algebra (which includes the special case Rep($$ \mathcal{H} $$ $H$G ) forG a finite group). We also specialize to the case that the fusion category is multiplicityfree. We discuss how to construct a modularinvariant partition function from a choice of Frobenius algebra structure on . We discuss how ordinary$$ {\mathcal{H}}^{\ast } $$ ${H}^{\ast}$G orbifolds for finite groupsG are a special case of the construction, corresponding to the fusion category Vec(G ) = Rep(ℂ[G ]^{*}). For the cases Rep(S _{3}), Rep(D _{4}), and Rep(Q _{8}), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S _{3}), Rep(D _{4}), Rep(Q _{8}), and , and discuss applications in$$ \textrm{Rep}\left({\mathcal{H}}_8\right) $$ $\mathrm{Rep}\left({H}_{8}\right)$c = 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially.