This content will become publicly available on December 1, 2023
 Award ID(s):
 1914934
 Publication Date:
 NSFPAR ID:
 10388303
 Journal Name:
 Journal of High Energy Physics
 Volume:
 2022
 Issue:
 12
 ISSN:
 10298479
 Sponsoring Org:
 National Science Foundation
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A bstract We formulate a series of conjectures relating the geometry of conformal manifolds to the spectrum of local operators in conformal field theories in d > 2 spacetime dimensions. We focus on conformal manifolds with limiting points at infinite distance with respect to the Zamolodchikov metric. Our central conjecture is that all theories at infinite distance possess an emergent higherspin symmetry, generated by an infinite tower of currents whose anomalous dimensions vanish exponentially in the distance. Stated geometrically, the diameter of a noncompact conformal manifold must diverge logarithmically in the higherspin gap. In the holographic context our conjectures are related to the Distance Conjecture in the swampland program. Interpreted gravitationally, they imply that approaching infinite distance in moduli space at fixed AdS radius, a tower of higherspin fields becomes massless at an exponential rate that is bounded from below in Planck units. We discuss further implications for conformal manifolds of superconformal field theories in three and four dimensions.

A bstract We argue for a relation between the supersymmetry breaking scale and the measured value of the dark energy density Λ. We derive it by combining two quantum gravity consistency swampland constraints, which tie the dark energy density Λ and the gravitino mass M 3 / 2 , respectively, to the mass scale of a light KaluzaKlein tower and, therefore, to the UV cutoff of the effective theory. Whereas the constraint on Λ has recently led to the Dark Dimension scenario, with a prediction of a single mesoscopic extra dimension of the micron size, we use the constraint on M 3 / 2 to infer the implications of such a scenario for the scale of supersymmetry breaking. We find that a natural scale for supersymmetry signatures is $$ M=\mathcal{O}\left({\Lambda}^{\frac{1}{8}}\right)=\mathcal{O}\left(\textrm{TeV}\right). $$ M = O Λ 1 8 = O TeV . This mass scale is within reach of LHC and of the next generation of hadron colliders. Finally, we discuss possible string theory and effective supergravity realizations of the Dark Dimension scenario with broken supersymmetry.

In this paper, we propose a new Swampland condition, the TransPlanckian Censorship Conjecture (TCC), based on the idea that in a consistent quantum theory of gravity subPlanckian quantum fluctuations should remain quantum and never become larger than the Hubble horizon and freeze in an expanding universe. Applied to the case of scalar fields, it leads to conditions that are similar to the refined dS Swampland conjecture. For large field ranges, TCC is stronger than the dS Swampland conjecture but it is weaker for small field ranges. In particular for asymptotic regions of field space, TCC leads to a bound V′≥2(d−1)(d−2)√V, which is consistent with all known cases in string theory. Like the dS Swampland conjecture, the TCC forbids longlived metastable dS spaces, but it does allow sufficiently shortlived ones.

Abstract We prove that
depth local random quantum circuits with two qudit nearestneighbor gates on a$${{\,\textrm{poly}\,}}(t) \cdot n^{1/D}$$ $\phantom{\rule{0ex}{0ex}}\text{poly}\phantom{\rule{0ex}{0ex}}\left(t\right)\xb7{n}^{1/D}$D dimensional lattice withn qudits are approximatet designs in various measures. These include the “monomial” measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was due to Brandão–Harrow–Horodecki (Commun Math Phys 346(2):397–434, 2016) for$${{\,\textrm{poly}\,}}(t)\cdot n$$ $\phantom{\rule{0ex}{0ex}}\text{poly}\phantom{\rule{0ex}{0ex}}\left(t\right)\xb7n$ . We also improve the “scrambling” and “decoupling” bounds for spatially local random circuits due to Brown and Fawzi (Scrambling speed of random quantum circuits, 2012). One consequence of our result is that assuming the polynomial hierarchy ($$D=1$$ $D=1$ ) is infinite and that certain counting problems are$${{\,\mathrm{\textsf{PH}}\,}}$$ $\phantom{\rule{0ex}{0ex}}\mathrm{PH}\phantom{\rule{0ex}{0ex}}$ hard “on average”, sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constantdepth quantum circuits was known to be hard for classical computers under these assumptions. However the standard strategy for extending this hardness result to approximate sampling requires the quantum circuits to have a property called “anticoncentration”, meaning roughly that the output has nearmaximal entropy. Unitary 2designs have the desired anticoncentration property. Our result improves the required depth for this level of anticoncentration from linear depthmore »$$\#{\textsf{P}}$$ $\#P$ 
A bstract We compute 1 /λ corrections to the fourpoint functions of halfBPS operators in SU( N ) $$ \mathcal{N} $$ N = 4 superYangMills theory at large N and large ’t Hooft coupling λ = $$ {g}_{\mathrm{YM}}^2N $$ g YM 2 N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S 4 free energy, which was computed at leading order in large N and to all orders in 1 /λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1 /λ corrections to higher derivative corrections to supergravity for scattering amplitudes of KaluzaKlein scalars in IIB string theory on AdS 5 × S 5 , which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R 4 interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D 4 R 4 order. Combined with constraints from [1], our results can be used to derive CFT data to oneloop D 4 R 4 order. Finally, we use AdS/CFT to fix these correlators in themore »