<p>We investigate the large-<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>N</mi></mrow></math> limit of the Berenstein-Maldacena-Nastase (BMN) matrix model with classical bosonic membranes which have spherical topologies and spin inside the 11-dimensional maximally supersymmetric plane-wave background. First we classify all possible M2-brane configurations based on the distribution of their components inside the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>×</mo><mi>S</mi><mi>O</mi><mo stretchy="false">(</mo><mn>6</mn><mo stretchy="false">)</mo></math> symmetric plane-wave spacetime. We then formulate a number of simple but very representative <i>Ansätze</i> of dielectric tops that rotate in this space. We examine the leading-order radial and angular/multipole stability for a wide range of these configurations. By analyzing perturbations at the next-to-leading order, we find that they exhibit the phenomenon of turbulent cascading of instabilities. Thereby, long-wavelength perturbations generate higher-order multipole instabilities through their nonlinear couplings.</p>

Greece

Minos Axenides

Emmanuel Floratos

South Korea

Georgios Linardopoulos

Turbulent aspects of Berenstein-Maldacena-Nastase membrane dynamics

We develop a new method to calculate finite size corrections for form factors in two-dimensional integrable quantum field theories. We extract these corrections from the excited state expectation value of bilocal operators in the limit when the operators are far apart. We elaborate the finite size effects explicitly up to the 3rd Lüscher order and conjecture the structure of the general form. We also fully recover the explicitly known massive fermion finite volume form factors.

Hungary

Zoltan Bajnok

Sweden

Istvan Szecsenyi

Istvan Vona

Finite volume form factors in integrable theories

We compute type-B Weyl anomaly coefficients for the domain wall version of <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM that is holographically dual to the D3-D5 probe-brane system with flux. Our starting point is the explicit expression for the improved energy momentum tensor of <math><mi>N</mi><mo>=</mo><mn>4</mn></math> SYM. We determine the two-point function of this operator in the presence of the domain wall and extract the anomaly coefficients from the result. In the same process we determine the two-point function of the displacement operator.

Ireland

Marius de Leeuw

Denmark

Charlotte Kristjansen

Germany

Matthias Volk

B-type anomaly coefficients for the D3-D5 domain wall

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.

George Georgiou

United States

Dimitrios Zoakos

Holographic correlators of semiclassical states in defect CFTs

ABJM theory in the presence of a half-BPS domain wall is dual to the D2-D4 probe brane system with nonzero worldvolume flux. The ABJM domain wall was recently shown to be integrable to lowest order in perturbation theory and bond dimension. In the present paper we show that the string theory dual of this system is integrable, namely that the string boundary conditions on the probe D4-brane preserve the integrability of the Green-Schwarz sigma model. Our result suggests that the ABJM domain wall is integrable to all loop orders and for any value of the bond dimension.

String integrability of the ABJM defect

We study the leading- (LO) and the next-to-leading-order (NLO) stability of multipole perturbations for a static dielectric M2-brane with spherical topology in the 11-dimensional maximally supersymmetric plane-wave background. We observe a cascade of instabilities that originates from the dipole (<math><mi>j</mi><mo>=</mo><mn>1</mn></math>) and quadrupole (<math><mi>j</mi><mo>=</mo><mn>2</mn></math>) sectors (the only unstable sectors of the LO) and propagates toward all the multipoles of the NLO.

Dimitrios Katsinis

Cascade of instabilities in the classical limit of the Berenstein-Maldacena-Nastase matrix model

The D3-D5 probe-brane system is holographically dual to a defect CFT which is known to be integrable. The evidence comes mainly from the study of correlation functions at weak coupling. In the present work we shed light on the emergence of integrability on the string theory side. We do so by constructing the double row transfer matrix which is conserved when the appropriate boundary conditions are imposed. The corresponding reflection matrix turns out to be dynamical and depends both on the spectral parameter and the string embedding coordinates.

Konstantin Zarembo

String integrability of defect CFT and dynamical reflection matrices

Using considerations based on the thermodynamical Bethe ansatz as well as the representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the SO(6) spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of $$ \mathfrak{so} $$ (5). The latter play the role of boundary states in a domain wall version of $$ \mathcal{N} $$ = 4 SYM theory which has non-vanishing, SO(5) symmetric vacuum expectation values on one side of a codimension 1 wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.

Marius Leeuw

Tamás Gombor

Balázs Pozsgay

Spin chain overlaps and the twisted Yangian

We explore the stability of a recently found class of spinning dielectric M2 branes in the 11-dimensional maximally supersymmetric plane-wave background. We find two small windows of instabilities in the dipole (<math><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow></math>) and quadrupole (<math><mi>j</mi><mo>=</mo><mn>2</mn></math>) sector of linear multipole perturbations.

Multipole stability of spinning M2 branes in the classical limit of the Berenstein-Maldacena-Nastase matrix model

We determine in a closed form all scalar one-point functions of the defect CFT dual to the D3–D5 probe brane system with k units of flux which amounts to calculating the overlap between a Bethe eigenstate of the integrable SO(6) spin chain and a certain matrix product state of bond dimension k. In particular, we show that the matrix product state is annihilated by all the parity odd charges of the spin chain which has recently been suggested as the criterion for such a state to correspond to an integrable initial state. Finally, we discuss the properties of the analogous matrix product state for the SO(5) symmetric D3–D7 probe brane set-up.