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1. Averaging over Narain moduli space

   https://doi.org/10.1007/JHEP10(2020)187  

   Maloney, Alexander; Witten, Edward (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract Recent developments involving JT gravity in two dimensions indicate that under some conditions, a gravitational path integral is dual to an average over an ensemble of boundary theories, rather than to a specific boundary theory. For an example in one dimension more, one would like to compare a random ensemble of two-dimensional CFT’s to Einstein gravity in three dimensions. But this is difficult. For a simpler problem, here we average over Narain’s family of two-dimensional CFT’s obtained by toroidal compactification. These theories are believed to be the most general ones with their central charges and abelian current algebra symmetries, so averaging over them means picking a random CFT with those properties. The average can be computed using the Siegel-Weil formula of number theory and has some properties suggestive of a bulk dual theory that would be an exotic theory of gravity in three dimensions. The bulk dual theory would be more like U(1) 2 D Chern-Simons theory than like Einstein gravity. 

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2. Exploring the strong-coupling region of SU(N) Seiberg-Witten theory

   https://doi.org/10.1007/JHEP11(2022)102  

   D’Hoker, Eric; Dumitrescu, Thomas T.; Nardoni, Emily (November 2022, Journal of High Energy Physics)

   A bstract We consider the Seiberg-Witten solution of pure $$ \mathcal{N} $$ N = 2 gauge theory in four dimensions, with gauge group SU( N ). A simple exact series expansion for the dependence of the 2( N − 1) Seiberg-Witten periods a I ( u ) , a DI ( u ) on the N − 1 Coulomb-branch moduli u n is obtained around the ℤ 2 N -symmetric point of the Coulomb branch, where all u n vanish. This generalizes earlier results for N = 2 in terms of hypergeometric functions, and for N = 3 in terms of Appell functions. Using these and other analytical results, combined with numerical computations, we explore the global structure of the Kähler potential K = $$ \frac{1}{2}{\sum}_I $$ 1 2 ∑ I Im( $$ \overline{a} $$ a ¯ I a DI ), which is single valued on the Coulomb branch. Evidence is presented that K is a convex function, with a unique minimum at the ℤ 2 N -symmetric point. Finally, we explore candidate walls of marginal stability in the vicinity of this point, and their relation to the surface of vanishing Kähler potential. 

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3. Sharpening the Distance Conjecture in diverse dimensions

   https://doi.org/10.1007/JHEP12(2022)114  

   Etheredge, Muldrow; Heidenreich, Ben; Kaya, Sami; Qiu, Yue; Rudelius, Tom (December 2022, Journal of High Energy Physics)

   A bstract The Distance Conjecture holds that any infinite-distance limit in the scalar field moduli space of a consistent theory of quantum gravity must be accompanied by a tower of light particles whose masses scale exponentially with proper field distance ‖ ϕ ‖ as m ~ exp(− λ ‖ ϕ ‖), where λ is order-one in Planck units. While the evidence for this conjecture is formidable, there is at present no consensus on which values of λ are allowed. In this paper, we propose a sharp lower bound for the lightest tower in a given infinite-distance limit in d dimensions: λ ≥ $$ 1/\sqrt{d-2} $$ 1 / d − 2 . In support of this proposal, we show that (1) it is exactly preserved under dimensional reduction, (2) it is saturated in many examples of string/M-theory compactifications, including maximal supergravity in d = 4 – 10 dimensions, and (3) it is saturated in many examples of minimal supergravity in d = 4 – 10 dimensions, assuming appropriate versions of the Weak Gravity Conjecture. We argue that towers with λ < $$ 1/\sqrt{d-2} $$ 1 / d − 2 discussed previously in the literature are always accompanied by even lighter towers with λ ≥ $$ 1/\sqrt{d-2} $$ 1 / d − 2 , thereby satisfying our proposed bound. We discuss connections with and implications for the Emergent String Conjecture, the Scalar Weak Gravity Conjecture, the Repulsive Force Conjecture, large-field inflation, and scalar field potentials in quantum gravity. In particular, we argue that if our proposed bound applies beyond massless moduli spaces to scalar fields with potentials, then accelerated cosmological expansion cannot occur in asymptotic regimes of scalar field space in quantum gravity. 

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4. 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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5. Spontaneous breaking of U(1) symmetry in coupled complex SYK models

   https://doi.org/10.1007/JHEP11(2020)162  

   Klebanov, Igor R.; Milekhin, Alexey; Tarnopolsky, Grigory; Zhao, Wenli (November 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract As shown in [1], two copies of the large N Majorana SYK model can produce spontaneous breaking of a Z 2 symmetry when they are coupled by appropriate quartic terms. In this paper we similarly study two copies of the complex SYK model coupled by a quartic term preserving the U(1) × U(1) symmetry. We also present a tensor counterpart of this coupled model. When the coefficient α of the quartic term lies in a certain range, the coupled large N theory is nearly conformal. We calculate the scaling dimensions of fermion bilinear operators as functions of α . We show that the operator $$ {c}_{1i}^{\dagger }{c}_{2i} $$ c 1 i † c 2 i , which is charged under the axial U(1) symmetry, acquires a complex dimension outside of the line of fixed points. We derive the large N Dyson-Schwinger equations and show that, outside the fixed line, this U(1) symmetry is spontaneously broken at low temperatures because this operator acquires an expectation value. We support these findings by exact diagonalizations extrapolated to large N . 

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