We propose a new class of holographic dualities between certain, generically non supersymmetric, defect conformal field theories (dCFTs) and their gravity duals. Our construction interpolates between the 1/2-BPS D3-D3 system and its field theory dual at one end, and the holographic duality presented in [1] at the other. On the gravity side, the defect is realised by a novel D5 probe brane embedded in the $\textit{AdS}$ × $\textit{S}$ geometry. The symmetry of the induced on the D5 brane metric is $\textit{AdS}$ × $\textit{S}$ × $\textit{S}$ . At a certain limit the D5 brane becomes singular and resembles the D3-D3 system. Consistency requires the presence of two D7 branes on which the D5 brane terminates. The existence of boundaries induces a gauge anomaly for the D5 brane which is cancelled through anomaly inflow from the D7 branes. The full system of the D5 and D7 branes is, thus, anomaly free. Also it does not have any tachyonic instabilities for a certain range of its parameters. On the field theory side, we determined the classical solution of the $$ \mathcal{N} $$ = 4 SYM equations of motion which we conjecture to describe the defect dual to the D5-D7 system and comment on the identification of the parameters appearing at the two sides of the duality.

Greece

George Georgiou

Dimitrios Zoakos

Holographic interpolations of defect CFTs

We propose and study a new holographic duality between a non-supersymmetric defect conformal field theory (dCFT) and its gravity dual. On the gravity side, the defect is realised by a novel solution of a D5 probe brane embedded in the $\textit{AdS}$ × $\textit{S}$ geometry. The D5 brane wraps an $\textit{S}$ ⊂ $\textit{S}$ and carries $\textit{k}$ units of flux through the $\textit{S}$ . The symmetry of the induced on the brane metric is $\textit{AdS}$ × $\textit{S}$ × $\textit{S}$ . The brane ends on an $\textit{ℝ}$ subspace of the 4-dimensional $\textit{AdS}$ boundary resulting to a codimension-2 defect. We first prove that our brane configuration is stable by showing that the masses of all the fluctuations of the transverse to the brane coordinates respect the B-F bound. On the field theory side, the 2-dimensional defect is described by a classical solution whose precise form we determine. Subsequently, we calculate the one-point functions of the energy-momentum tensor and of the chiral primary operators (CPOs), first at strong and then at weak coupling. In an appropriate limit, we find compelling agreement between the weak and strong coupling results. Furthermore, we also extract one of the B-type Weyl anomaly coefficients.

China

South Korea

Georgios Linardopoulos

Holography of a novel codimension-2 defect CFT

In contradistinction to the case of massive excitations, the connection between integrability and the tree-level massless scattering matrix of integrable $\textit{σ}$-models is lost. Namely, in well-known 2-d integrable models the tree-level massless S-matrix exhibits particle production and fails to factorise. This is conjectured to happen due to IR ambiguities in the massless tree-level amplitudes. We present a definition of the massless S-matrix which has all the nice properties of integrable theories, there is no particle production and the S-matrix factorises. Our definition works for the large class of $\textit{σ}$-models with one or more isometries. As an example, we present in detail the case of the SU(2) principal chiral model (PCM).

The massless S-matrix of integrable $\textit{σ}$-models

Particle production in integrable field theories may exist depending on the vacuum around which excitations are defined. To tackle this and analogous issues with conventional field theoretical tools, we consider the integrable λ-deformed model for <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math> together with a timelike coordinate. We construct the corresponding four-dimensional plane wave background (a deformation of the Nappi–Witten solution) keeping also post-plane wave corrections, as well as all the non-trivial λ-dependence. After imposing the classical light-cone gauge and the Virasoro constraints, we obtain an interacting field theory for the transverse physical modes which are massive. We explicitly demonstrate the absence of particle production to leading order in the large k-expansion. This is based crucially on the form of the interaction vertices and their dependence on the λ-deformation parameter. In addition, we compute the S-matrix for the two-particle elastic scattering exactly in λ and to leading order in the large k-expansion. Our method can be applied to any integrable theory with at least one isometry in order to check the classical integrability of the parent theory.

CERN

Konstantinos Sfetsos

Scattering in integrable pp-wave backgrounds: -matrix and Absence of Particle Production

We calculate holographically three-point functions of scalar operators with large dimensions at finite density and finite temperature. To achieve this, we construct new solutions that involve two isometries of the deformed internal space. The novel feature of these solutions is that the corresponding two-point function depends not only on the conformal dimension but also on the difference between the two angular momenta. After identifying the dual operators, we systematically calculate three-point correlators as an expansion in powers of the temperature and the chemical potential. Our analytic perturbative results are in agreement with the exact numerical computation. The three point correlator (when the background contains either temperature or density but not both) is always a monotonic function of the temperature or the chemical potential. However, when both parameters are present the three point correlator is no longer a monotonic function. For fixed finite temperature and small values of the chemical potential a minimum of the three-point function appears. Surprisingly, contributions from the internal space do not depend on the chemical potential or the temperature, as long as those are treated as perturbations.

United States

Holographic three-point correlators at finite density and temperature

We set up the computation of correlation functions for operators that are dual to semiclassical string states in strongly coupled defect conformal field theories (dCFTs). In the dCFT that is dual to the D3-D5 probe-brane system, we calculate the correlation function of two heavy operators perturbatively, in powers of the conformal ratio. We find that the leading term agrees with the prediction of the operator product expansion (OPE). In the case of two heavy Berenstein-Maldacena-Nastase operators, we find agreement in subleading orders as well.

Hungary

Holographic correlators of semiclassical states in defect CFTs

We calculate holographically one and two-point functions of scalar operators at finite density and/or finite temperature. In the case of finite density and zero temperature we argue that only scalar operators can have non-zero VEVs. In the case in which both the chemical potential and the temperature are finite, we present a systematic expansion of the two-point correlators in powers of the temperature T and the chemical potential Ω.

Holographic correlation functions at finite density and/or finite temperature

We construct and thoroughly study a new integrable example of the AdS/CFT correspondence with Schrödinger symmetry. On the gravity side, the supergravity solution depends on two parameters and is obtained by marginally deforming the internal space of the Schrödinger background through a series of TsT transformations. On the field theory side, we identify the dual field theory which also depends on two parameters.

Germany

Georgios Itsios

Marginally deformed Schrödinger/dipole CFT correspondence

We present the Hamiltonian formulation of the recently constructed integrable theories of [49]. These theories turn out to be canonically equivalent to the sum of an asymmetrically gauged CFT and of the most general λ-deformed model of [21]. Using the Hamiltonian formalism, we prove that the full set of conserved charges of the models of [49] are in involution, ensuring their Hamiltonian integrability. Finally, we show that the equations of motion of these theories can be put in the form of zero curvature Lax connections.

Hamiltonian integrability of the webs of integrable theories

We present an intuitive diagrammatic representation of a new class of integrable σ-models. It is shown that to any given diagram corresponds an integrable theory that couples N WZW models with a certain number of each of the following four fundamental integrable models, the PCM, the YB model, both based on a group G, the isotropic σ-model on the symmetric space <math><mi>G</mi><mo>/</mo><mi>H</mi></math> and the YB model on the symmetric space <math><mi>G</mi><mo>/</mo><mi>H</mi></math>. To each vertex of a diagram we assign the matrix of one of the aforementioned fundamental integrable theories. Any two vertices may be connected with a number of lines having an orientation and carrying an integer level <math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math>. Each of these lines is associated with an asymmetrically gauged WZW model at an arbitrary level <math><msub><mrow><mi>k</mi></mrow><mrow><mi>i</mi></mrow></msub></math>. Gauge invariance of the full action is translated to level conservation at the vertices. We also show how to immediately read from the diagrams the corresponding σ-model actions. The most generic of these models depends on at least <math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mn>1</mn></math> parameters, where n is the total number of vertices/fundamental integrable models. Finally, we discuss the case where the level conservation at the vertices is relaxed and the case where the deformation matrix is not diagonal in the space of integrable models.