We analyse dynamics of the closed Type IIA and IIB string on various tri-vector deformed background searching for signatures of integrability. Using numerical methods we construct Poincaré sections for particular embeddings of the string and show that these are not destroyed under tri-vector deformation. We find that the corresponding Lyapunov exponents decay showing that trajectories do not diverge.

Russia

Edvard Musaev

Gleb Zverev

On integrability of tri-vector deformed Type II string

We extend the formalism of tri-vector deformations to the full SL(5) exceptional field theory with no truncation assumed thus covering 11D backgrounds of any form. We derive explicit transformation rules for 11D supergravity component fields and prove that these generate solutions given the same algebraic conditions hold: generalized Yang–Baxter equation and the unimodularity condition.

Sergei Barakin

Kirill Gubarev

Tri-vector deformations with external fluxes

We develop a formalism of poly-vector deformations for Type IIB backgrounds with a block diagonal metric and non-vanishing self-dual 5-form RR field strength. Making use of the embedding of the Type IIB theory into the  $$\textrm{E}_{6(6)}$$  <math> <msub> <mtext>E</mtext> <mrow> <mn>6</mn> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </msub> </math>   exceptional field theory we derive explicit transformation rules for four-vector deformations. We prove that the algebraic condition following from the Type IIB realization of exceptional Drinfeld algebras is sufficient for the transformation to generate a solution.

Timophey Petrov

Polyvector deformations of Type IIB backgrounds

In this work we focus on the study of RG flows of conformal field theories that are holographically dual to Poincaré domain wall solutions in  $$D=3$$  <math> <mrow> <mi>D</mi> <mo>=</mo> <mn>3</mn> </mrow> </math>  ,  $$\mathcal {N}=(2,0)$$  <math> <mrow> <mi>N</mi> <mo>=</mo> <mo>(</mo> <mn>2</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </math>   gauged supergravity coupled to a sigma model with target space  $$\textrm{SU}(1, 1)/\textrm{U}(1) = \mathbb {H}^2$$  <math> <mrow> <mtext>SU</mtext> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mtext>U</mtext> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mrow> <mi>H</mi> </mrow> <mn>2</mn> </msup> </mrow> </math>  . This theory is truncated to a subsector where the vector field and phase of the scalar field vanish and we consider different boundary conditions for the remaining real scalar field. The RG flows, which are mostly non-superysymmetric, are analyzed by treating the supergravity field equations as a dynamical system for the scalar field and its derivative with respect to the scale factor. Phase diagrams are constructed for different values of the parameter  $$a^2$$  <math> <msup> <mi>a</mi> <mn>2</mn> </msup> </math>  , which is related to the curvature of the scalar manifold. The behavior of solutions near the boundary is used to determine their type based on the expansion of the corresponding fake superpotential. By incorporating information on the boundary conditions, the obtained RG flows are interpreted using the holographic dictionary. Numerical solutions and plots of the fake superpotential are also provided.

JINR

Ksenia Arkhipova

Lev Astrakhantsev

Türkiye

Nihat Deger

Anastasia Golubtsova

Holographic RG flows and boundary conditions in a 3D gauged supergravity

Classical Yang–Baxter equation governing bi-vector deformations of 10d supergravity is known to have no solutions along non-abelian compact isometries. By providing explicit examples we show that this is in contrast to generalized Yang–Baxter equation governing tri-vector deformations of 11d supergravity. We present deformations of the AdS $${}_7\times \mathbb {S}^4$$  <math> <mrow> <msub> <mrow></mrow> <mn>7</mn> </msub> <mo>×</mo> <msup> <mrow> <mi>S</mi> </mrow> <mn>4</mn> </msup> </mrow> </math>   and flat backgrounds with isometries generated by Killing vectors of a sphere. Isometries of the AdS space-time are preserved by such deformations.

Tri-vector deformations on compact isometries

In Bakhmatov et al. (Phys. Rev. D 105(8): L081904, 2022) we presented a modification of 11-dimensional supergravity field equations which upon dimensional reduction yields generalized supergravity equations in 10-dimensions. In this paper we provide full technical details of that result which is based on SL(5) exceptional field theory. The equations are obtained by making a non-unimodular tri-vector Yang-Baxter deformation which breaks the initial local diffeomorphism symmetry in 11 dimensions down to separate coordinate transformations in external 7 and internal 4 directions. We also give some non-trivial solutions to these equations.

Ilya Bakhmatov

Aybike Çatal-Özer

Generalized 11D supergravity equations from tri-vector deformations

We construct the full effective action including DBI and WZ terms for solitonic 5-branes covariant under T-duality. The result is a completion of results known in the literature to a full T-duality covariant expression. The covariant WZ action includes previously omitted R–R terms. The obtained full covariant effective action reproduces the one obtained by S-duality from the D5-brane upon the correct choice of the covariant charge.

Jeffrey Molina

The invariant action for solitonic 5-branes

Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non-geometric. Comparison with alternative treatment based on sigma models on supercosets shows consistency.

Non-abelian fermionic T-duality in supergravity

A truncation of the SL(5) Exceptional Field Theory that allows to describe spacetimes of the form × with the 4-form flux on is constructed. The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS × $$\mathbbm{S}$$ solution of = 11 supergravity. We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS × $$\mathbbm{S}$$ .

Armenia

Non-abelian tri-vector deformations in

We show how the Wess-Zumino terms of the different branes in string theory can be embedded within double field theory. Crucial ingredients in our construction are the identification of the correct brane charge tensors and the use of the double field theory potentials that arise from dualizing the standard double field theory fields. This leads to a picture where under T-duality the brane does not change its worldvolume directions but where, instead, it shows different faces depending on whether some of the worldvolume and/or transverse directions invade the winding space. As a non-trivial by-product we show how the different Wess-Zumino terms are modified when the brane propagates in a background with a non-zero Romans mass parameter. Furthermore, we show that for non-zero mass parameter the brane creation process, when one brane passes through another brane, gets generalized to brane configurations that involve exotic branes as well.