We describe a field theoretic formulation for one-dimensional string theory. It is given by the collective representation of matrix model and leads to physical interpretation theory as that massless scalar in two dimensions. The additional dimension, coming from large-N color model, has an extent which goes infinity continuum limit. interactions are non-zero only at boundaries this dimension.

In this paper we compute the low energy absorption cross section for minimally coupled massles scalars and spin- $1/2$ particles into a general spherically symmetric black hole in arbitrary dimensions. The have equal to area of hole, while give measured flat spatial metric conformally related true metric.

We show that the spectrum of SYK model can be interpreted as a 3D scalar coupled to gravity. The has mass which is at Breitenholer-Freedman bound AdS$_2$, and subject delta function potential center interval along third direction. This, through Kaluza-Klein procedure on AdS$_2 \times (S^1)/Z_2$, generates reproducing bi-local propagator strong coupling. Furthermore, leading $1/J$ correction calculated in this picture reproduces known poles propagator, providing credence conjecture bulk dual...

A bstract In this work, we formulate a path-integral optimization for two dimensional conformal field theories perturbed by relevant operators. We present several evidences how mechanism works, based on calculations in free as well general arguments of RG flows theories. Our is performed minimizing the complexity functional that depends metric and also couplings. Then, compute optimal perturbatively find it agrees with time slice hyperbolic scalar AdS/CFT correspondence. Last but not least,...

We propose that the Euclidean bilocal collective field theory of critical large-N vector models provides a complete definition proposed dual higher spin fields in anti--de Sitter spaces. show how this can be decomposed into an infinite number even one more dimension. The has nontrivial classical solution which leads to $O(N)$ thermodynamic entropy characteristic lower dimensional theory, as required by general considerations holography. A subtle cancellation coming from bulk dimension with...

The non-perturbative formulation of 2-dimensional quantum gravity in terms the large-N limit matrix models is studied to include effects higher order curvature terms. This leads whose potential contains a symmetry breaking term form Tr ϕAϕA, where A given fixed matrix. d = 0 dimensions and effectively induces additional ( ϕ k ) 2 one potential. An exact solution leading V(ϕ) 1/2 + g/N 4 g′/N presented 3 phases: γ −1/2 (smooth surfaces), (branched polymer) 1/3 (intermediate phase). Including...

We construct a family of solutions in IIB supergravity theory. These are time-dependent or depend on light-like coordinate and can be thought as deformations ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$. Several the have singularities. The preserve 8 supersymmetries. argue that these dual to $\mathcal{N}=4$ gauge theory $3+1$ dimensional space-time with metric coupling is varying time direction, respectively. This identification allows us map question singularity resolution

We study the time evolution of a conformal field theory deformed by relevant operator under smooth but fast quantum quench which brings it to point. argue that when scale δt is small compared set coupling, expectation value quenched scales universally as δλ/δt(2Δ-d), where δλ amplitude. This growth further enhanced logarithmic factor in even dimensions. present explicit results for free scalar and fermionic theories, supported an analytic understanding leading contribution quenches. Our...

We expand on the investigation of universal scaling properties in early time behaviour fast but smooth quantum quenches a general d-dimensional conformal field theory deformed by relevant operator dimension Δ with time-dependent coupling. The quench consists changing coupling from an initial constant value λ 1 amount order δλ to some other final 2, over scale δt. In limit where δt is smaller than all length scales problem, ≪ 1/() , 2 1/(Δ − d), energy (density) injected into system as δℰ ∼...

The equation of motion the tachyon field is obtained by requiring conformal invariance closed bosonic string propagator in a background. cubic coupling also this way. These equations are generalizations Kosterlitz-Thouless flow and involve nonperturbative contributions to $\ensuremath{\beta}$ functions.

We consider the question of identifying bulk space-time SYK model. Focusing on signature emergent (Euclidean) model, we explain need for non-local (Radon-type) transformations external legs $n$-point Green's functions. This results in a dual theory with Euclidean AdS additional leg-factors. speculate that these factors incorporate coupling states similar to discrete 2d string theory.

In \url{arXiv:1704.07208} it was shown that the spectrum and bilocal propagator of SYK model with four fermion interactions can be realized as a three dimensional in $AdS_2 \times S^1/Z_2$ nontrivial boundary conditions additional dimension. this paper we show similar picture holds for generalizations $q$-fermion interactions. The 3D realization is now given on space whose metric conformal to subject non-trivial potential addition delta function at center interval. It Horava-Witten...

We examine the spectrum of small vibrations giant gravitons when expand in anti--de Sitter space and they on sphere. For any given angular harmonic, modes are found to have frequencies related curvature length scale background; these independent radius (and hence momentum) brane itself. This implies that holographic dual theory must have, a R charge sector, low-lying non-BPS excitations with level spacings charge.

We argue that the gauge theory dual to type IIB string in a ten-dimensional $\mathrm{pp}$-wave background resides on Euclidean subspace spanning four of eight transverse coordinates. then show evolution along one light cone directions bulk is identifiable as RG flow theory, relation facilitating ``holography'' background. The reorganizes into theories defined over Hilbert subspaces fixed R charge. reorganization breaks $\mathrm{SO}(4,2)\ifmmode\times\else\texttimes\fi{}\mathrm{SO}(6)$...

This is a pedagogical review of some aspects quantum field theories in the limit which number internal degrees freedom large. The focus on large-$N$ QCD. authors briefly discuss several well-known approaches to solution $N=\ensuremath{\infty}$ limit: loop equations, classical actions, and master fields. Eguchi-Kawai models are discussed detail, recently obtained numerical results reviewed.

We consider the $N=4$ super Yang-Mills theory in flat $3+1$-dimensional space-time with a time dependent coupling constant which vanishes at $t=0$, like ${g}_{\mathrm{YM}}^{2}={t}^{p}$. In an analogous quantum mechanics toy model we find that response is singular. The energy diverges for generic state. addition, if $p>1$ phase of wave function has wildly oscillating behavior, does not allow it to be continued past $t=0$. A similar effect would make gauge singular as well, though nontrivial...

Quantum quenches display universal scaling in several regimes. For which start from a gapped phase and cross critical point, with rate slow compared to the initial gap, many systems obey Kibble-Zurek scaling. More recently, different behaviour has been shown occur when quench is fast all other physical scales, but still UV cutoff. We investigate passage scalar fermionic free field theories time dependent masses for dynamics can be solved exactly rates. find that renormalized one point...