arXiv subjects

George Georgiou

Publications and source records attributed to George Georgiou.

At least 37 records · Page 2Linked to original sources

arXiv2019

$λ$-deformations of left-right asymmetric CFTs

We compute the all-loop anomalous dimensions of current and primary field operators in deformed current algebra theories based on a general semi-simple group, but with different (large) levels for the left and right sectors. These theories, unlike their equal level counterparts, possess a new non-trivial fixed point in the IR. By computing the exact in $λ$ two- and three-point functions for these operators we deduce their OPEs and their equal-time commutators. Using these we argue on the nature of the CFT at the IR fixed point. The associated to the currents Poisson brackets are a two-parameter deformation of the canonical structure of the isotropic PCM.

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arXiv2019

Double and cyclic $λ$-deformations and their canonical equivalents

We prove that the doubly lambda-deformed sigma-models, which include integrable cases, are canonically equivalent to the sum of two single lambda-deformed models. This explains the equality of the exact beta-functions and current anomalous dimensions of the doubly lambda-deformed sigma-models to those of two single lambda-deformed models. Our proof is based upon agreement of their Hamiltonian densities and of their canonical structure. Subsequently, we show that it is possible to take a well defined non-Abelian type limit of the doubly-deformed action. Last, but not least, by extending the above, we construct multi-matrix integrable deformations of an arbitrary number of WZW models.

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arXiv2019

The exact $C$-function in integrable $λ$-deformed theories

By employing CFT techniques, we show how to compute in the context of λ-deformations of current algebras and coset CFTs the exact in the deformation parameters C-function for a wide class of integrable theories that interpolate between a UV and an IR point. We explicitly consider RG flows for integrable deformations of left-right asymmetric current algebras and coset CFTs. In all cases, the derived exact C-functions obey all the properties asserted by Zamolodchikov's c-theorem in two-dimensions.

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arXiv2019

Field theory and $λ$-deformations: Expanding around the identity

We explore the structure of the $λ$-deformed $σ$-model action by setting up a perturbative expansion around the free field point corresponding to the identity group element. We include all field interaction terms up to sixth order. We compute the two- and three-point functions of current and primary filed operators, their anomalous dimensions as well as the $β$-function for the $λ$-parameter. Our results are in complete agreement with those obtained previously using gravitational and/or CFT perturbative methods in conjunction with the non-perturbative symmetry, as well as with those obtained using methods exploiting the geometry defined in the space of couplings. The advantage of this approach is that all deformation effects are already encoded in the couplings of the interaction vertices and in the $λ$-dressed operators.

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arXiv2019

Exact results from the geometry of couplings and the effective action

We invent a method that exploits the geometry in the space of couplings and the known all-loop effective action, in order to calculate the exact in the couplings anomalous dimensions of composite operators for a wide class of integrable $σ$-models. These involve both self and mutually interacting current algebra theories. We work out the details for important classes of such operators. In particular, we consider the operators built solely from an arbitrary number of currents of the same chirality, the composite operators which factorize into a chiral and an anti-chiral part, as well as those made up of three currents of mixed chirality. Remarkably enough, the anomalous dimensions of the former two sets of operators turn out to vanish. In our approach, loop computations are completely avoided.

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arXiv2019

String theory on the Schrodinger pp-wave background

We study string theory on the pp-wave geometry obtained by taking the Penrose limit around a certain null geodesic of the non-supersymmetric Schrodinger background. We solve for the spectrum of bosonic excitations and find compelling agreement with the dispersion relation of the giant magnons in the Schrodinger background obtained previously in arXiv:1712.03091. Inspired by the pp-wave spectrum we conjecture an exact in the t'Hooft coupling dispersion relation for the magnons in the original Schrodinger background. We show that the pp-wave background admits exactly 16 Killing spinors. We use the explicit form of the latter in order to derive the supersymmetry algebra of the background which explicitly depends on the deformation parameter. Its bosonic subalgebra is of the Newton-Hooke type.

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arXiv2019

Integrable Lorentz-breaking deformations and RG flows

We construct the all loop effective action for WZW models perturbed by current-bilinear terms of the type $J_+J_- $, $J_+J_+ $ and $J_-J_- $, the last two of which explicitly break Lorentz invariance. For isotropic couplings we prove integrability. For the case in which only the first two terms are present we identify a non-perturbative symmetry of the effective action and we compute the exact beta-functions. These become identically zero outside a bounded region in the parametric space.

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arXiv2018

The most general $λ$-deformation of CFTs and integrability

We show that the CFT with symmetry group $G_{k_1}\times G_{k_2}\times \cdots \times G_{k_n}$ consisting of WZW models based on the same group $G$, but at arbitrary integer levels, admits an integrable deformation depending on $2(n-1)$ continuous parameters. We derive the all-loop effective action of the deformed theory and prove integrability. We also calculate the exact in the deformation parameters RG flow equations which can be put in a particularly simple compact form. This allows a full determination and classification of the fixed points of the RG flow, in particular those that are IR stable. The models under consideration provide concrete realizations of integrable flows between CFTs. We also consider non-Abelian T-duality type limits.

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arXiv2018

Novel all loop actions of interacting CFTs: Construction, integrability and RG flows

We construct the all loop effective action representing, for small couplings, simultaneously self and mutually interacting current algebra CFTs realized by WZW models. This non-trivially generalizes our previous works where such interactions were, at the linear level, not simultaneously present. For the two coupling case we prove integrability and calculate the coupled RG flow equations. We also consider non-Abelian T-duality type limits. Our models provide concrete realisations of integrable flows between exact CFTs and exhibit several new features which we discuss in detail.

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arXiv2018

Holographic three-point correlators in the Schrodinger/dipole CFT correspondence

We calculate, for the first time, three-point correlation functions involving "heavy" operators in the Schrodinger/null-dipole CFT correspondence at strong coupling. In particular, we focus on the three-point functions of the dilaton modes and two "heavy" operators. The heavy states are dual to the single spin and dyonic magnon, the single spin and dyonic spike solutions or to two novel string solutions which do not have an undeformed counterpart. Our results provide the leading term of the correlators in the large $λ$ expansion and are in perfect agreement with the form of the correlator dictated by non-relativistic conformal invariance. We also specify the scaling function which can not be fixed by using conformal invariance.

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arXiv2017

Giant magnons and spiky strings in the Schrodinger/dipole-deformed CFT correspondence

We construct semi-classical string solutions of the Schrödinger $Sch_5 \times S^5$ spacetime, which is conjectured to be the gravity dual of a non-local dipole-deformed CFT. They are the counterparts of the giant magnon and spiky string solutions of the undeformed $AdS_5 \times S^5$ to which they flow when the deformation parameter is turned off. They live in an $S^3$ subspace of the five-sphere along the directions of which the $B$-field has non-zero components having also extent in the $Sch_5$ part of the metric. Finally, we speculate on the form of the dual field theory operators.

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arXiv2017

Integrable flows between exact CFTs

We explicitly construct families of integrable $σ$-model actions smoothly interpolating between exact CFTs. In the ultraviolet the theory is the direct product of two current algebras at levels $k_1$ and $k_2$. In the infrared and for the case of two deformation matrices the CFT involves a coset CFT, whereas for a single matrix deformation it is given by the ultraviolet direct product theories but at levels $k_1$ and $k_2-k_1$. For isotropic deformations we demonstrate integrability. In this case we also compute the exact beta-function for the deformation parameters using gravitational methods. This is shown to coincide with previous results obtained using perturbation theory and non-perturbative symmetries.

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arXiv2017

A new class of integrable deformations of CFTs

We construct a new class of integrable $σ$-models based on current algebra theories for a general semisimple group $G$ by utilizing a left-right asymmetric gauging. Their action can be thought of as the all-loop effective action of two independent WZW models for $G$ both at level $k$, perturbed by current bilinears mixing the different WZW models. A non-perturbative symmetry in the couplings parametric space is revealed. We perform the Hamiltonian analysis of the action and demonstrate integrability in several cases. We extend our construction to deformations of $G/H$ CFTs and show integrability when $G/H$ is a symmetric space. Our method resembles that used for constructing the $λ$-deformed integrable $σ$-models, but the results are distinct and novel.

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arXiv2017

Quantum aspects of doubly deformed CFTs

We study quantum aspects of the recently constructed doubly lambda-deformed sigma-models representing the effective action of two WZW models interacting via current bilinears. We show that although the exact beta-functions and current anomalous dimensions are identical to those of the lambda-deformed models, this is not true for the anomalous dimensions of generic primary field operators in accordance with the fact that the two models differ drastically. Our proofs involve CFT arguments, as well as effective sigma-model action and gravity calculations.

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arXiv2016

Entanglement Entropy of the N=4 SYM spin chain

We present a detailed study of the Entanglement Entropy (EE) of excited states in all closed rank one subsectors of N=4 SYM, namely SU(2), SU(1|1) and SL(2). Exploiting the techniques of the Coordinate and the Algebraic Bethe Ansatz we obtain the EE for spin chains with up to seven magnons, at leading order in the coupling expansion but exact in the length of the spin chain and of the part of it that we cut. Focusing on the superconformal primary operator with two magnons in the BMN limit, we derive analytic and exact, in the coupling $λ'$, expressions for the Renyi and the EE. The interpolating functions for the Renyi and the EE monotonically increase as the coupling increases from the weak coupling $λ' \rightarrow 0$ regime to the strong coupling $λ' \rightarrow \infty$ regime. This results to a violation of a certain bound for the EE that is present at weak coupling and confirms the physical intuition that entanglement increases when the coupling increases.

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arXiv2016

All-loop correlators of integrable $λ$-deformed $σ$-models

We compute the 2- and 3-point functions of currents and primary fields of $λ$-deformed integrable $σ$-models characterized also by an integer $k$. Our results apply for any semisimple group $G$, for all values of the deformation parameter $λ$ and up to order $1/k$. We deduce the OPEs and equal-time commutators of all currents and primaries. We derive the currents' Poisson brackets which assume Rajeev's deformation of the canonical structure of the isotropic PCM, the underlying structure of the integrable $λ$-deformed $σ$-models. We also present analogous results in two limiting cases of special interest, namely for the non-Abelian T-dual of the PCM and for the pseudodual model.

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arXiv2016

All-loop anomalous dimensions in integrable $λ$-deformed $σ$-models

We calculate the all-loop anomalous dimensions of current operators in $λ$-deformed $σ$-models. For the isotropic integrable deformation and for a semi-simple group $G$ we compute the anomalous dimensions using two different methods. In the first we use the all-loop effective action and in the second we employ perturbation theory along with the Callan-Symanzik equation and in conjunction with a duality-type symmetry shared by these models. Furthermore, using CFT techniques we compute the all-loop anomalous dimensions of bilinear currents for the isotropic deformation case and a general $G$. Finally we work out the cases of anisotropic $SU(2)$ and the two coupling, corresponding to the symmetric coset $G/H$ and a subgroup $H$, splitting of a group $G$.

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arXiv2015

A new higher-spin theory of supergravity in 2+1 dimensions

We construct a novel higher-spin theory of gravity in 2+1 spacetime dimensions. The construction is based on a higher-spin super-algebra extending the Poincare group. Our algebra accommodates all integer and half-integer spins from 1 to infinity and, in contrast to the results in the existing literature, allows for an infinite number of particles of spin s. Subsequently, we generalise the construction to include a cosmological constant. In this case, the higher-spin group is an extension of the AdS or dS group and contains only bosonic generators. Treating the higher-spin groups as gauge groups we write down the Chern-Simons like action, the transformation laws for the fields of the theory and their equations of motion in each of the three aforementioned cases. Finally, we comment on the generalisation of our algebras in $d+1$ dimensions.

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