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1. Moduli spaces in CFT: large charge operators

   https://doi.org/10.1007/JHEP09(2024)185  

   Cuomo, Gabriel; Rastelli, Leonardo; Sharon, Adar (September 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> Using the large-charge expansion, we prove a necessary condition for a CFT to exhibit conformal symmetry breaking, under the assumption that a continuous global symmetry isalsobroken on the moduli space: there must be a tower of charged local operators whose scaling dimensions are asymptotically linear in the charge. In supersymmetric theories with a continuous R-symmetry and a holomorphic moduli space, the existence of such a tower of operators follows trivially from a BPS condition: their scaling dimensions are then exactly linear in the R-charge. We illustrate the more general statement in several examples of three-dimensional$$ \mathcal{N} $$ $N$= 1 CFTs, where the leading linear behavior receives nontrivial corrections. By considering a suitable scaling limit, we also relate the spectrum of states with large charge on the cylinder (isomorphic to local operators) to the spectrum of massive particles on the moduli space. 

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2. Species scale in diverse dimensions

   https://doi.org/10.1007/JHEP05(2024)112  

   van_de_Heisteeg, Damian; Vafa, Cumrun; Wiesner, Max; Wu, David H (May 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In a quantum theory of gravity, the species scale Λ_scan be defined as the scale at which corrections to the Einstein action become important or alternatively as codifying the “number of light degrees of freedom”, due to the fact that$$ {\Lambda}_s^{-1} $$ ${\Lambda }_s^{-1}$is the smallest size black hole described by the EFT involving only the Einstein term. In this paper, we check the validity of this picture in diverse dimensions and with different amounts of supersymmetry and verify the expected behavior of the species scale at the boundary of moduli space. This also leads to the evaluation of the species scale in the interior of the moduli space as well as to the computation of the diameter of the moduli space. We also find evidence that the species scale satisfies the bound$$ {\frac{\left|\nabla {\Lambda}_s\right|}{\Lambda_s}}^2\le \frac{1}{d-2} $$ ${\frac{\left(\nabla {\Lambda }_s\right)}{{\Lambda }_s}}^2\le \frac{1}{d-2}$all over moduli space including the interior. 

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3. Free field realizations for rank-one SCFTs

   https://doi.org/10.1007/JHEP12(2024)004  

   Beem, Christopher; Deb, Anirudh; Martone, Mario; Meneghelli, Carlo; Rastelli, Leonardo (December 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> In this paper, we construct the associated vertex operator algebras for all$$ \mathcal{N} $$ $N$= 2 superconformal field theories of rank one. We give a uniform presentation through free-field realizations, which turns out to be a particularly suitable framework for this task. The elementary building blocks of the construction are dictated by the low energy degrees of freedom on the Higgs branch, which are well understood for rank-one theories. We further analyze the interplay between Higgs and Coulomb data on the moduli space of vacua, which tightly constrain the overall structure of the free field realizations. Our results suggest a plausible bottom-up classification scheme for low-rank SCFTs incorporating vertex algebra techniques. 

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4. Two loop mass renormalisation in heterotic string theory: NS states

   https://doi.org/10.1007/JHEP11(2023)052  

   Bhattacharya, Ritabrata (November 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> In this work computation of the renormalised mass at two loop order for the NS sector of heterotic string theory is attempted. We first implement the vertical integration prescription for choosing a section avoiding the spurious poles due to the presence of a required number of picture changing operators. As a result the relevant amplitude on genus 2 Riemann surface can be written as a boundary term. We then identify the 1PI region of the moduli space having chosen a gluing compatible local coordinates around the external punctures. We also identify the relevant integrands and the relevant region of integration for the modular parameters at the boundary. 

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5. Tree-level superstring amplitudes: the Neveu-Schwarz sector

   https://doi.org/10.1007/JHEP09(2024)008  

   Cacciatori, Sergio L; Grushevsky, Samuel; Voronov, Alexander A (September 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We present a complete computation of superstring scattering amplitudes at tree level, for the case of Neveu-Schwarz insertions. Mathematically, this is to say that we determine explicitly the superstring measure on the moduli space$$ {\mathcal{M}}_{0,n,0} $$ $M_{0,n,0}$of super Riemann surfaces of genus zero withn≥ 3 Neveu-Schwarz punctures. While, of course, an expression for the measure was previously known, we do this from first principles, using the canonically defined super Mumford isomorphism [1]. We thus determine the scattering amplitudes, explicitly in the global coordinates on$$ {\mathcal{M}}_{0,n,0} $$ $M_{0,n,0}$, without the need for picture changing operators or ghosts, and are also able to determine canonically the value of the coupling constant. Our computation should be viewed as a step towards performing similar analysis on$$ {\mathcal{M}}_{0,0,n} $$ $M_{0,0,n}$, to derive explicit tree-level scattering amplitudes with Ramond insertions. 

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