Non-critical Theory Research Articles

Toverline{T} deformations, massive gravity and non-critical strings

The Toverline{T} deformation of a 2 dimensional field theory living on a curved space- time is equivalent to coupling the undeformed field theory to 2 dimensional ‘ghost-free’ massive gravity. We derive the equivalence classically, and using a path integral formulation of the random geometries proposal, which mirrors the holographic bulk cutoff picture. We emphasize the role of the massive gravity Stückelberg fields which describe the diffeomorphism between the two metrics. For a general field theory, the dynamics of the Stückelberg fields is non-trivial, however for a CFT it trivializes and becomes equivalent to an additional pair of target space dimensions with associated curved target space geometry and dynamical worldsheet metric. That is, the Toverline{T} deformation of a CFT on curved spacetime is equivalent to a non-critical string theory in Polyakov form, with a non-zero B-field. We give a direct proof of the equivalence classically without relying on gauge fixing, and determine the explicit form for the classical Hamiltonian of the Toverline{T} deformation of an arbitrary CFT on a curved spacetime. When the QFT action is a sum of a CFT plus an operator of fixed scaling dimension, as for example in the sine-Gordon model, the equivalence to a non-critical theory string holds with a modified target space metric and modified B-field. Finally we give a stochastic path integral formulation for the general Toverline{T}+Joverline{T}+Toverline{J} deformation of a general QFT, and show that it reproduces a recent path integral proposal in the literature.

Anisotropic coupling of gravity and electromagnetism in Hořava-Lifshitz theory

We analyze the electromagnetic-gravity interaction in a pure Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz framework. To do so we formulate the Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity in $4+1$ dimensions and perform a Kaluza-Klein reduction to $3+1$ dimensions. We use this reduction as a mathematical procedure to obtain the $3+1$ coupled theory, which at the end is considered as a fundamental, self-consistent theory. The critical value of the dimensionless coupling constant in the kinetic term of the action is $\ensuremath{\lambda}=1/4$. It is the kinetic conformal point for the nonrelativistic electromagnetic-gravity interaction. In distinction, the corresponding kinetic conformal value for pure Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity in $3+1$ dimensions is $\ensuremath{\lambda}=1/3$. We analyze the geometrical structure of the critical and noncritical cases, they correspond to different theories. The physical degrees of freedom propagated by the noncritical theory are the transverse traceless graviton, the transverse gauge vector and two scalar fields. In the critical theory one of the scalars is absent, only the dilaton scalar field is present. The gravity and vector excitations propagate with the same speed, which at low energy can be taken to be the speed of light. The field equations for the gauge vector in the nonrelativistic theory have exactly the same form as the relativistic electromagnetic field equations arising from the Kaluza-Klein reduction of general relativity, and are equal to them for a particular value of one of the coupling constants. The potential in the Hamiltonian is a polynomial of finite degree in the gauge vector and its covariant derivatives.

“Socioanalisi”: primi elementi per una riformulazione della teoria sociale come analisi critica della sociazione

Starting from deep-rooted crisis of contemporary social sciences, we need to reformulate our theoretical approach in order to enhancing interpretative knowledge of our social realities. The first step of this analytic program is to deconstruct the historical paradigm of “critical theory” as a hypostatic way to explain social reality in its totality. From this perspective I propose a passage from “critical theory” to “socioanalysis” seen as an analytical-descriptive process without standardization. From this point of view the analysis of sociation (socioanalysis on the analogy of psychoanalysis) is always a critical approach to social reality because its explicative frame is not “prescriptive” but only “possible” (that is polyvalent). In this analytical context we have to confront with concept of ambivalence. This means that “things are in one way but they also are in another way”: existence, social life, interaction, agency, thought cannot be unequivocally interpreted. From this point of view I discuss two examples of contemporary theories that are implicitly ambivalent: the non-critical theory of Bruno Latour and the pragmatic theory of criticism of Luc Boltanski.

Local reversibility and entanglement structure of many-body ground states

The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. Here, we present a novel characterization of quantum states, which we call ‘local reversibility’. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new universal features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are relevant both to critical and non-critical theories.

A test of bosonization at the level of four-point functions in Chern-Simons vector models

We study four-point functions in Chern-Simons vector models in the large $N$ limit. We compute the four-point function of the scalar primary to all orders in the `t Hooft coupling $\lambda=N/k$ in $U(N)_k$ Chern-Simons theory coupled to a fundamental fermion, in both the critical and non-critical theory, for a particular case of the external momenta. These theories cover the entire 3-parameter "quasi-boson" and 2-parameter "quasi-fermion" families of 3-dimensional quantum field theories with a slightly-broken higher spin symmetry. Our results are consistent with the celebrated bosonization duality, as we explicitly verify by calculating four-point functions in the free critical and non-critical bosonic theories.

Modes of log gravity

The physical modes of a recently proposed $D$-dimensional ``critical gravity'', linearized about its anti-de Sitter vacuum, are investigated. All ``log mode'' solutions, which we categorize as ``spin-2'' or ``Proca'', arise as limits of the massive spin-2 modes of the noncritical theory. The linearized Einstein tensor of a spin-2 log mode is itself a `nongauge' solution of the linearized Einstein equations whereas the linearized Einstein tensor of a Proca mode takes the form of a linearized general coordinate transformation. Our results suggest the existence of a holographically dual logarithmic conformal field theory.

Topological string in harmonic space and correlation functions in [formula omitted] stringy cosmology

We develop the harmonic space method for conifold and use it to study local complex deformations of T * S 3 preserving manifestly SL ( 2 , C ) isometry. We derive the perturbative manifestly SL ( 2 , C ) invariant partition function Z top of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c = 1 noncritical theory are described by highest υ ( n , 0 ) and lowest components υ ( 0 , n ) of SL ( 2 , C ) spin s = n 2 multiplets ( υ ( n − k , k ) ) , 0 ⩽ k ⩽ n and are shown to be naturally captured by harmonic monomials. Isodoublets ( n = 1 ) describe uncoupled units of momentum and winding modes and are exactly realized as the SL ( 2 , C ) harmonic variables U α + and V α − . We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T * S 1 ( S 1 ) to the harmonic method on T * S 3 ( S 3 ). The manifestly SU ( 2 , C ) covariant correlation functions of the S 3 quantum cosmology model of Gukov–Saraikin–Vafa are also studied.

Boundary ground ring in 2D string theory

The 2D quantum gravity on a disc, or the non-critical theory of open strings, is known to exhibit an integrable structure, the boundary ground ring, which determines completely the boundary correlation functions. Inspired by the recent progress in boundary Liouville theory, we extend the ground ring relations to the case of non-vanishing boundary Liouville interaction known also as FZZT brane in the context of the 2D string theory. The ring relations yield an over-determined set of functional recurrence equations for the boundary correlation functions. The ring action closes on an infinite array of equally spaced FZZT branes for which we propose a matrix model realization. In this matrix model the boundary ground ring is generated by a pair of complex matrix fields.

2D gravity and the black hole solution in 2D critical string theory

We discuss the relation between 2D gravity and critical string theory in two target space dimensions. In particular we consider the effect that the tachyon, and its back reaction on the metric, has on the interpretation of the critical theory as a non-critical theory coupled to world sheet gravity. We examine the generalizations of the black hole solution of the critical theory and argue that a generic feature of these solutions is that they have two horizons, similar to, but distinct from, the Reissner-Nordstrøm black hole. We also find some indication that the tachyon may destabilize a naked singularity. Finally we show that KPZ scaling is valid for the general solution of the critical theory, when it is interpreted as a theory of world sheet gravity.

On localization in the theory of the quantized hall effect: A two-dimensional realization of the θ-vacuum

It is shown that the localization problem in the theory of the quantized Hall effect is governed by the zero-component grassmannian U(2 m) non-linear σ-model with θ-term, a two-dimensional analogue of the θ-vacuum in Yang-Mills theory. In this case, θ is to be interpreted as the “bare” value for the Hall conductivity, determined by an underlying non-critical theory. A detailed derivation is presented starting from the replica method and a delta function distribution for the impurities.