We build a novel time-like coset sigma-model describing type-II superstring theory in a charged rotating black-brane background that interpolates between a local AdS 3 in the IR and a linear-dilaton geometry in the UV. This allows one to peform a systematic study of holography in non-AdS backgrounds which are smoothly connected to AdS 3. We construct massless closed string states vertex operators in the NS-NS sector, calculate the corresponding two-point correlation functions, and discuss holographic interpretation of our results from 4+1 dimensional boundary field theory point of view. Compactifying the theory on 𝕋4, we show that the spectrum of a single long string with unit winding agrees with the spectrum of a CFT2 deformed by   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$ . We also calculate correlation functions of operators of the dual 1+1 dimensional non-conformal boundary field theory using worldsheet techniques.

France

Soumangsu Chakraborty

United States

Mikhail Goykhman

Solvable time-like cosets and holography beyond AdS

We calculate a set of conformal correlators in the critical <math><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> vector model in <math><mn>2</mn><mo>&lt;</mo><mi>d</mi><mo>&lt;</mo><mn>6</mn></math> dimensions. We focus on the correlators involving the Hubbard-Stratonovich field <math><mi>s</mi></math>, and its composite form <math><msup><mi>s</mi><mn>2</mn></msup></math>. In the process, we report a number of new calculations of diagrams involving the composite <math><msup><mi>s</mi><mn>2</mn></msup></math> operator. Through the calculation of the <math><mo>⟨</mo><msup><mi>s</mi><mn>2</mn></msup><msup><mi>s</mi><mn>2</mn></msup><mi>s</mi><mo>⟩</mo></math> three-point function, we shed new light on a conjectured <math><mi>s</mi><mo>→</mo><mo>−</mo><mi>s</mi></math> symmetry in the <math><mi>s</mi></math> sector of the critical <math><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> vector model in <math><mi>d</mi><mo>=</mo><mn>3</mn></math>.

Israel

Noam Chai

Ritam Sinha

Conformal correlators in the critical <math><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> vector model

We construct long-range fermionic models with the Gross-Neveu and Gross­Neveu-Yukawa interaction, and argue that their critical regimes are equivalent. To this end, we calculate various CFT data in ϵ- and 1/N-expansion, and demonstrate their agreement in the overlapping regimes of validity.

India

Long-range fermions and critical dualities

We study interacting critical UV regime of the long-range O(N) vector model with quartic coupling. Analyzing CFT data within the scope of ϵ- and 1/N-expansion, we collect evidence for the equivalence of this model and the critical IR limit of the cubic model coupled to a generalized free field O(N) vector multiplet.

Critical long-range vector model in the UV

We calculate various CFT data for the O(N) vector model with the long-range interaction, working at the next-to-leading order in the 1/N expansion. Our results provide additional evidence for the existence of conformal symmetry at the long-range fixed point, as well as the continuity of the CFT data at the long-range to short-range crossover point s  *  of the exponent parameter s. We also develop the N &gt; 1 generalization of the recently proposed IR duality between the long-range and the deformed short-range models, providing further evidence for its non-perturbative validity in the entire region d/2 &lt; s &lt; s  * .

Long-range vector models at large N

We calculate conformal field theory data for the Gross-Neveu model in <math><mn>2</mn><mo>&lt;</mo><mi>d</mi><mo>&lt;</mo><mn>4</mn></math> dimensions at the next-to-leading order in the <math><mn>1</mn><mo>/</mo><mi>N</mi></math> expansion. In particular, we make use of the background field method to derive various conformal triangles involving the composite operator <math><msup><mi>s</mi><mn>2</mn></msup></math>, for the Hubbard-Stratonovich field <math><mi>s</mi></math>. We then apply these conformal triangles to obtain the corresponding one-pion exchange coefficients.

CFT data in the Gross-Neveu model

We study perturbative renormalization of the composite operators in the   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$ -deformed two-dimensional free field theories. The pattern of renormalization for the stress-energy tensor is different in the massive and massless cases. While in the latter case the canonical stress tensor is not renormalized up to high order in the perturbative expansion, in the massive theory there are induced counterterms at linear order. For a massless theory our results match the general formula derived recently in [1].

Anshuman Dey

Michael Smolkin

Composite operators in   <math> <mi>T</mi> <mover> <mi>T</mi> <mo>¯</mo> </mover> </math>  $$ T\overline{T} $$ -deformed free QFTs

We use the background field method to systematically derive CFT data for the critical ϕ 6 vector model in three dimensions, and the Gross-Neveu model in dimensions 2 ≤ d ≤ 4. Specifically, we calculate the OPE coefficients and anomalous dimensions of various operators, up to next-to-leading order in the 1/N expansion.

Vladimir Rosenhaus

The background field method and critical vector models

We study behavior of the critical <math><mi>O</mi><mo>(</mo><mi>N</mi><mo>)</mo></math> vector model with quartic interaction in <math><mn>2</mn><mo>≤</mo><mi>d</mi><mo>≤</mo><mn>6</mn></math> dimensions to the next-to-leading order in the large-<math><mi>N</mi></math> expansion. We derive and perform consistency checks that provide an evidence for the existence of a nontrivial fixed point and explore the corresponding conformal field theory (CFT). In particular, we use conformal techniques to calculate the multiloop diagrams up to and including 4 loops in general dimension. These results are used to calculate a new CFT data associated with the three-point function of the Hubbard-Stratonovich field. In <math><mn>6</mn><mo>−</mo><mi>ε</mi></math> dimensions our results match their counterparts obtained within a proposed alternative description of the model in terms of <math><mi>N</mi><mo>+</mo><mn>1</mn></math> massless scalars with cubic interactions. In <math><mi>d</mi><mo>=</mo><mn>3</mn></math> we find that the operator product expansion coefficient vanishes up to <math><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msup><mi>N</mi><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></msup><mo>)</mo></math> order.

Vector model in various dimensions

We study global quenches in a number of interacting quantum field theory models away from the conformal regime. We conduct a perturbative renormalization at one-loop level and track the modifications of the quench protocol induced by the renormalization group flow. The scaling of various observables at early times is evaluated in the regime of rapid quench rates, with a particular emphasis placed on the leading order effects that cannot be recovered using the finite order conformal perturbation theory. We employ the canonical ideas of effective action to verify our results and discuss a potential route towards understanding the late time dynamics.