An official website of the United States government
A<sc>bstract</sc> We use a combination of analytical and numerical methods to study out-of-time order correlators (OTOCs) in the sparse Sachdev-Ye-Kitaev (SYK) model. We find that at a given order ofN, the standard result for theq-local, all-to-all SYK, obtained through the sum over ladder diagrams, is corrected by a series in the sparsity parameter,k. We present an algorithm to sum the diagrams at any given order of 1/(kq)n. We also study OTOCs numerically as a function of the sparsity parameter and determine the Lyapunov exponent. We find that numerical stability when extracting the Lyapunov exponent requires averaging over a massive number of realizations. This trade-off between the efficiency of the sparse model and consistent behavior at finiteNbecomes more significant for larger values ofN.
more »
« less
This content will become publicly available on December 1, 2025
Systematics of U-spin sum rules for systems with direct sums
A<sc>bstract</sc> A rich mathematical structure underlying flavor sum rules has been discovered recently. In this work, we extend these findings to systems with a direct sum of representations. We prove several results for the general case. We derive an algorithm that enables the determination of allU-spin amplitude sum rules at arbitrary order of the symmetry breaking for any system containing a direct sum of the representations 0 ⨁ 1. Potential applications are numerous and include, for example, higher order sum rules for CP-violating charm decays with an arbitrary number of final states.
more »
« less
- Award ID(s):
- 2309456
- PAR ID:
- 10621666
- Publisher / Repository:
- Journal of High Energy Physics
- Date Published:
- Journal Name:
- Journal of High Energy Physics JHEP
- Volume:
- 2024
- Issue:
- 12
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
A<sc>bstract</sc> We review the effective field theory (EFT) bootstrap by formulating it as an infinite-dimensional semidefinite program (SDP), built from the crossing symmetric sum rules and the S-matrix primal ansatz. We apply the program to study the large-Nchiral perturbation theory (χPT) and observe excellent convergence of EFT bounds between the dual (rule-out) and primal (rule-in) methods. This convergence aligns with the predictions of duality theory in SDP, enabling us to analyze the bound states and resonances in the ultra-violet (UV) spectrum. Furthermore, we incorporate the upper bound of unitarity to uniformly constrain the EFT space from the UV scaleMusing the primal method, thereby confirming the consistency of the large-Nexpansion. In the end, we translate the large-N χPT bounds to constrain the higher derivative corrections of holographic QCD models.more » « less
-
A<sc>bstract</sc> In this paper we develop a Young diagram approach to constructing higher dimensional operators formed from massless superfields and their superderivatives in$$ \mathcal{N} $$ = 1 supersymmetry. These operators are in one-to-one correspondence with non-factorizable terms in on-shell superamplitudes, which can be studied with massless spinor helicity techniques. By relating all spin-helicity variables to certain representations under a hidden U(N) symmetry behind the theory, we show each non-factorizable superamplitude can be identified with a specific Young tableau. The desired tableau is picked out of a more general set of U(N) tensor products by enforcing the supersymmetric Ward identities. We then relate these Young tableaux to higher dimensional superfield operators and list the rules to read operators directly from Young tableau. Using this method, we present several illustrative examples.more » « less
-
A<sc>bstract</sc> We extend the Effective Field Theory of Heavy Dark Matter to arbitrary odd representations of SU(2) and incorporate the effects of bound states. This formalism is then deployed to compute the gamma-ray spectrum for a5of SU(2): quintuplet dark matter. Except at isolated values of the quintuplet mass, the bound state contribution to hard photons with energy near the dark-matter mass is at the level of a few percent compared to that from direct annihilation. Further, compared to smaller representations, such as the triplet wino, the quintuplet can exhibit a strong variation in the shape of the spectrum as a function of mass. Using our results, we forecast the fate of the thermal quintuplet, which has a mass of ~13.6 TeV. We find that existing H.E.S.S. data should be able to significantly test the scenario, however, the final word on this canonical model of minimal dark matter will likely be left to the Cherenkov Telescope Array (CTA).more » « less
-
A<sc>bstract</sc> Dark matter scattering off a nucleus has a small probability of inducing an observable ionization through the inelastic excitation of an electron, called the Migdal effect. We use an effective field theory to extend the computation of the Migdal effect in semiconductors to regions of small momentum transfer to the nucleus, where the final state of the nucleus is no longer well described by a plane wave. Our analytical result can be fully quantified by the measurable dynamic structure factor of the semiconductor, which accounts for the vibrational degrees of freedom (phonons) in a crystal. We show that, due to the sum rules obeyed by the structure factor, the inclusive Migdal rate and the shape of the electron recoil spectrum is well captured by approximating the nuclei in the crystal as free ions; however, the exclusive differential rate with respect to energy depositions to the crystal depends on the phonon dynamics encoded in the dynamic structure function of the specific material. Our results now allow the Migdal effect in semiconductors to be evaluated even for the lightest dark matter candidates (mχ≳ 1 MeV) that can kinematically excite electrons.more » « less
