Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe bi-conical vector model at $1/N$
115
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We study finite $N$ aspects of the $O(m)times O(N-m)$ vector model with quartic interactions in general $2leq d leq 6$ spacetime dimensions. This model has recently been shown to display the phenomenon of persistent symmetry breaking at a perturbative Wilson-Fisher-like fixed point in $d=4-epsilon$ dimensions. The large rank limit of the bi-conical model displays a conformal manifold and a moduli space of vacua. We find a set of three double trace scalar operators that are respectively irrelevant, relevant and marginal deformations of the conformal manifold in general $d$. We calculate the anomalous dimensions of the single and multi-trace scalar operators to the first sub-leading order in the large rank expansion. The anomalous dimension of the marginal operator does not vanish in general, indicating that the conformal manifold is lifted at finite $N$. In the case of equal ranks we are able to derive explicitly the scaling dimensions of various operators as functions of only $d$.
rate research
Read More
We compute the $O(1/N^3)$ correction to the critical exponent $eta$ in the chiral XY or chiral Gross-Neveu model in $d$-dimensions. As the leading order vertex anomalous dimension vanishes, the direct application of the large $N$ conformal bootstrap formalism is not immediately possible. To circumvent this we consider the more general Nambu-Jona-Lasinio model for a general non-abelian Lie group. Taking the abelian limit of the exponents of this model produces those of the chiral XY model. Subsequently we provide improved estimates for $eta$ in the three dimensional chiral XY model for various values of $N$.
The SYK model has a wormhole-like solution after averaging over the fermionic coupling in the nearly $AdS_2$ space. Even when the couplings are fixed the contribution of these wormholes continues to exist and new saddle points appear which are interpreted as half-wormholes. In this paper, we will study the fate of these wormholes in a model without quenched disorder namely a tensor model with $O(N)^{q-1}$ gauge symmetry whose correlation function and thermodynamics in the large $N$ limit are the same as that of SYK model. We will restate the factorization problem linked with the wormhole threaded Wilson, operator, in terms of global charges or non-trivial cobordism classes associated with disconnected wormholes. Therefore in order for the partition function to factorize especially at short distances, there must exist certain topological defects which break the global symmetry associated with wormholes and make the theory devoid of global symmetries. We will interpret these wormholes with added topological defects as our half-wormholes. We will also comment on the late time behaviour of the spectral form factor, particularly its leading and sub-leading order contributions coming from higher genus wormholes in the gravitational sector. We also found its underlying connections with the Brownian SYK model, particularly in the plateau region which has constant contributions coming from non-trivial saddle points of holonomy from the wormhole followed by an exponential rising part, where the other non-trivial saddles from half-wormhole dominate and give rise to unusual thermodynamics in the bulk sector due to non-perturbative effects.
We continue the study of the Sachdev-Ye-Kitaev model in the Large $N$ limit. Following our formulation in terms of bi-local collective fields with dynamical reparametrization symmetry, we perform perturbative calculations around the conformal IR point.
We show analytically that the spectral density of the $q$-body Sachdeev-Ye-Kitaev (SYK) model agrees with that of Q-Hermite polynomials with Q a non-trivial function of $q ge 2$ and the number of Majorana fermions $N gg 1$. Numerical results, obtained by exact diagonalization, are in excellent agreement with the analytical spectral density even for relatively small $N sim 8$. For $N gg 1$ and not close to the edge of the spectrum, we find the macroscopic spectral density simplifies to $rho(E) sim exp[2arcsin^2(E/E_0)/log eta]$, where $eta$ is the suppression factor of the contribution of intersecting Wick contractions relative to nested contractions. This spectral density reproduces the known result for the free energy in the large $q$ and $N$ limit. In the infrared region, where the SYK model is believed to have a gravity-dual, the spectral density is given by $rho(E) sim sinh[2pi sqrt 2 sqrt{(1-E/E_0)/(-log eta)}]$. It therefore has a square-root edge, as in random matrix ensembles, followed by an exponential growth, a distinctive feature of black holes and also of low energy nuclear excitations. Results for level-statistics in this region confirm the agreement with random matrix theory. Physically this is a signature that, for sufficiently long times, the SYK model and its gravity dual evolve to a fully ergodic state whose dynamics only depends on the global symmetry of the system. Our results strongly suggest that random matrix correlations are a universal feature of quantum black holes and that the SYK model, combined with holography, may be relevant to model certain aspects of the nuclear dynamics.
The nature of the deconfining phase transition in the 2+1-dimensional SU(N) Georgi-Glashow model is investigated. Within the dimensional-reduction hypothesis, the properties of the transition are described by a two-dimensional vectorial Coulomb gas models of electric and magnetic charges. The resulting critical properties are governed by a generalized SU(N) sine-Gordon model with self-dual symmetry. We show that this model displays a massless flow to an infrared fixed point which corresponds to the Z$_N$ parafermions conformal field theory. This result, in turn, supports the conjecture of Kogan, Tekin, and Kovner that the deconfining transition in the 2+1-dimensional SU(N) Georgi-Glashow model belongs to the Z$_N$ universality class.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
