A supersymmetric SYK model with a curious low energy behavior

Biggs, Anna; Maldacena, Juan; Narovlansky, Vladimir

doi:10.1007/JHEP08(2024)124

A supersymmetric SYK model with a curious low energy behavior

Anna Biggs
(
- Princeton U.
)
,
Juan Maldacena
(
- Princeton, Inst. Advanced Study
)
,
Vladimir Narovlansky
(
- Princeton U.
)

Sep 15, 2023

48 pages

Published in:

JHEP 08 (2024) 124

Published: Aug 16, 2024

e-Print:

2309.08818 [hep-th]

DOI:

10.1007/JHEP08(2024)124

View in:

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Abstract: (Springer)

We consider

\mathcal{N}

= 2, 4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like S = S

_{0}

+ (constant)T

^{a}

, where a ≠ 1. The large N equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.

Note:

v2: minor changes

Extended Supersymmetry
M(atrix) Theories
Random Systems
energy: low
supersymmetry: 4
spin: glass
field theory: scalar
symmetry breaking
fluctuation
matrix model

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