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1. $$ \mathcal{N} $$ = 2 JT supergravity and matrix models

   https://doi.org/10.1007/JHEP12(2023)003  

   Turiaci, Gustavo J. ; Witten, Edward ( December 2023 , Journal of High Energy Physics)

   Generalizing previous results for$$ \mathcal{N} $$$N$= 0 and$$ \mathcal{N} $$$N$= 1, we analyze$$ \mathcal{N} $$$N$= 2 JT supergravity on asymptotically AdS₂spaces 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 differentR-charge are statistically independent and each is described by its own$$ \mathcal{N} $$$N$= 2 random matrix ensemble. We also analyze the case with a time-reversal symmetry, either commuting or anticommuting with theR-charge. In order to compare supergravity to random matrix theory, we develop an$$ \mathcal{N} $$$N$= 2 analog of the recursion relations for Weil-Petersson volumes originally discovered by Mirzakhani in the bosonic case.

    

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2. When left and right disagree: entropy and von Neumann algebras in quantum gravity with general AlAdS boundary conditions

   https://doi.org/10.1007/JHEP08(2024)010  

   Marolf, Donald ; Zhang, Daiming ( August 2024 , Journal of High Energy Physics)

   Euclidean path integrals for UV-completions ofd-dimensional bulk quantum gravity were recently studied in [1] by assuming that they satisfy axioms of finiteness, reality, continuity, reflection-positivity, and factorization. Sectors$$ {\mathcal{H}}_{\mathcal{B}} $$$H_B$of the resulting Hilbert space were then defined for any (d− 2)-dimensional surface$$ \mathcal{B} $$$B$, 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 unionB⊔Bof two identical (d− 2)-dimensional surfacesBwere studied in detail and, after the inclusion of finite-dimensional ‘hidden sectors,’ were shown to provide a Hilbert space interpretation of the associated Ryu-Takayanagi entropy. The analysis was performed by constructing type-I von Neumann algebras$$ {\mathcal{A}}_L^B $$$A_L^B$,$$ {\mathcal{A}}_R^B $$$A_R^B$that act respectively at the left and right copy ofBinB⊔B.

   Below, we consider the case of general$$ \mathcal{B} $$$B$, and in particular for$$ \mathcal{B} $$$B$=B_L⊔B_RwithB_L,B_Rdistinct. For anyB_R, we find that the von Neumann algebra atB_Lacting on the off-diagonal Hilbert space sector$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$$H_{B_L\bigsqcup B_R}$is a central projection of the corresponding type-I von Neumann algebra on the ‘diagonal’ Hilbert space$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$$H_{B_L\bigsqcup B_L}$. As a result, the von Neumann algebras$$ {\mathcal{A}}_L^{B_L} $$$A_L^{B_L}$,$$ {\mathcal{A}}_R^{B_L} $$$A_R^{B_L}$defined in [1] using the diagonal Hilbert space$$ {\mathcal{H}}_{B_L\bigsqcup {B}_L} $$$H_{B_L\bigsqcup B_L}$turn out to coincide precisely with the analogous algebras defined using the full Hilbert space of the theory (including all sectors$$ {\mathcal{H}}_{\mathcal{B}} $$$H_B$). A second implication is that, for any$$ {\mathcal{H}}_{B_L\bigsqcup {B}_R} $$$H_{B_L\bigsqcup B_R}$, including the same hidden sectors as in the diagonal case again provides a Hilbert space interpretation of the Ryu-Takayanagi entropy. We also show the above central projections to satisfy consistency conditions that lead to a universal central algebra relevant to all choices ofB_LandB_R.

    

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3. A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)

   https://doi.org/10.1007/JHEP04(2024)140  

   Colafranceschi, Eugenia ; Marolf, Donald ; Wang, Zhencheng ( April 2024 , Journal of High Energy Physics)

   The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de 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 operatorsA, Bwill satisfy the trace inequality Tr(AB) ≤ Tr(A)Tr(B). This relation holds on any Hilbert space$$ \mathcal{H} $$$H$and is deeply associated with the fact that the algebraB($$ \mathcal{H} $$$H$) 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 semi-classical expansion and with arbitrary higher-derivative 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 Jackiw-Teitelboim gravity and we also motivate it for more general theories.

    

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4. Ward identities for superamplitudes

   https://doi.org/10.1007/JHEP06(2024)035  

   Kallosh, Renata ( June 2024 , Journal of High Energy Physics)

   We introduce Ward identities for superamplitudes inD-dimensional$$ \mathcal{N} $$$N$-extended supergravities. These identities help to clarify the relation between linearized superinvariants and superamplitudes. The solutions of these Ward identities for ann-partice superamplitude take a simple universal form for half BPS and non-BPS amplitudes. These solutions involve arbitrary functions of spinor helicity and Grassmann variables for each of thensuperparticles. The dimension of these functions at a given loop order is exactly the same as the dimension of the relevant superspace Lagrangians depending on half-BPS or non-BPS superfields, given by (D− 2)L+ 2 −$$ \mathcal{N} $$$N$or (D− 2)L+ 2 −$$ 2\mathcal{N} $$$2N$, respectively. This explains why soft limits predictions from superamplitudes and from superspace linearized superinvariants agree.

    

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5. Notes on gauging noninvertible symmetries. Part I. Multiplicity-free cases

   https://doi.org/10.1007/JHEP02(2024)154  

   Perez-Lona, A ; Robbins, D ; Sharpe, E ; Vandermeulen, T ; Yu, X ( February 2024 , Journal of High Energy Physics)

   In this paper we discuss gauging noninvertible zero-form symmetries in two dimensions. We specialize to certain gaugeable cases, specifically, fusion categories of the form$$ \textrm{Rep}\left(\mathcal{H}\right) $$$\mathrm{Rep}\left(H\right)$for$$ \mathcal{H} $$$H$a suitable Hopf algebra (which includes the special case Rep(G) forGa finite group). We also specialize to the case that the fusion category is multiplicity-free. We discuss how to construct a modular-invariant partition function from a choice of Frobenius algebra structure on$$ {\mathcal{H}}^{\ast } $$$H^{\ast }$. We discuss how ordinaryGorbifolds for finite groupsGare a special case of the construction, corresponding to the fusion category Vec(G) = Rep(ℂ[G]^*). For the cases Rep(S₃), Rep(D₄), and Rep(Q₈), we construct the crossing kernels for general intertwiner maps. We explicitly compute partition functions in the examples of Rep(S₃), Rep(D₄), Rep(Q₈), and$$ \textrm{Rep}\left({\mathcal{H}}_8\right) $$$\mathrm{Rep}\left(H_8\right)$, and discuss applications inc= 1 CFTs. We also discuss decomposition in the special case that the entire noninvertible symmetry group acts trivially.

    

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