14 research outputs found
Double-scaled SYK and de Sitter Holography
We propose a new model of low dimensional de Sitter holography in the form of
a pair of double-scaled SYK models at infinite temperature coupled via an equal
energy constraint . As a test of the duality, we compute the two-point
function between two dressed SYK operators that preserve the
constraint. We find that in the large limit, the two-point function
precisely matches with the Green's function of a massive scalar field of mass
squared in a 3D de Sitter space-time with radius
. In this correspondence, the SYK time is
identified with the proper time difference between the two operators. We
introduce a candidate gravity dual of the doubled SYK model given by a JT/de
Sitter gravity model obtained via a circle reduction from 3D Einstein-de Sitter
gravity. We comment on the physical meaning of the finite de Sitter temperature
and entropy.Comment: 26 pages, 4 figure
Towards a full solution of the large N double-scaled SYK model
We compute the exact, all energy scale, 4-point function of the large
double-scaled SYK model, by using only combinatorial tools and relating the
correlation functions to sums over chord diagrams. We apply the result to
obtain corrections to the maximal Lyapunov exponent at low temperatures. We
present the rules for the non-perturbative diagrammatic description of
correlation functions of the entire model. The latter indicate that the model
can be solved by a reduction of a quantum deformation of SL, that
generalizes the Schwarzian to the complete range of energies.Comment: 52+28 pages, 14 figures; v2: references revised, typos corrected,
changed normalization of SL(2)_q 6j symbo
A supersymmetric SYK model with a curious low energy behavior
We consider = 2, 4 supersymmetric SYK models that have a
peculiar low energy behavior, with the entropy going like , where . The large 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
Quantum groups, non-commutative , and chords in the double-scaled SYK model
We study the double-scaling limit of SYK (DS-SYK) model and elucidate the
underlying quantum group symmetry. The DS-SYK model is characterized by a
parameter , and in the and low-energy limit it goes over to
the familiar Schwarzian theory. We relate the chord and transfer-matrix picture
to the motion of a ``boundary particle" on the Euclidean Poincar{\'e} disk,
which underlies the single-sided Schwarzian model. carries an action of
,
and we argue that the symmetry of the full DS-SYK model is a certain
-deformation of the latter, namely . We do this by obtaining the effective
Hamiltonian of the DS-SYK as a (reduction of) particle moving on a lattice
deformation of , which has this algebra as its symmetry. We also exhibit the
connection to non-commutative geometry of -homogeneous spaces, by obtaining
the effective Hamiltonian of the DS-SYK as a (reduction of) particle moving on
a non-commutative deformation of . There are families of possibly
distinct -deformed spaces, and we point out which are relevant for
the DS-SYK model.Comment: 70 pages, 6 figure
Multi-trace Correlators in the SYK Model and Non-geometric Wormholes
We consider multi-energy level distributions in the SYK model, and in
particular, the role of global fluctuations in the density of states of the SYK
model. The connected contributions to the moments of the density of states go
to zero as , however, they are much larger than the standard RMT
correlations. We provide a diagrammatic description of the leading behavior of
these connected moments, showing that the dominant diagrams are given by 1PI
cactus graphs, and derive a vector model of the couplings which reproduces
these results. We generalize these results to the first subleading corrections,
and to fluctuations of correlation functions. In either case, the new set of
correlations between traces (i.e. between boundaries) are not associated with,
and are much larger than, the ones given by topological wormholes. The
connected contributions that we discuss are the beginning of an infinite series
of terms, associated with more and more information about the ensemble of
couplings, which hints towards the dual of a single realization. In particular,
we suggest that incorporating them in the gravity description requires the
introduction of new, lighter and lighter, fields in the bulk with fluctuating
boundary couplings.Comment: 81 pages, 23 figures. V2: added short discussion on the modified dip
time, and corrected minor typo
Dualities between fermionic theories and the Potts model
Abstract We show that a large class of fermionic theories are dual to a q β 0 limit of the Potts model in the presence of a magnetic field. These can be described using a statistical model of random forests on a graph, generalizing the (unrooted) random forest description of the Potts model with only nearest neighbor interactions. We then apply this to find a statistical description of a recently introduced family of OSp(1|2M) invariant field theories that provide a UV completion to sigma models with the same symmetry