arXiv subjects

Edvard T. Musaev

Publications and source records attributed to Edvard T. Musaev.

At least 37 records · Page 2Linked to original sources

arXiv2021

Non-abelian U-duality at work

Non-abelian U-duality originates from the construction of exceptional Drinfel'd algebra (EDA), which extends the constriction of the classical Drinfel'd double. This symmetry is a natural extension of Poisson--Lie T-duality and is believed to be a symmetry of Type II string/M-theory or their low-energy effective theories. In this paper, we consider non-abelian U-dualities of 11- or 10-dimensional backgrounds starting with E${}_{n(n)}$ EDA with $n\leq 6$ with vanishing trombone gauging. The latter guarantees that all dual backgrounds satisfy the standard supergravity equations of motion. In particular, when the duality includes a timelike T-duality, we obtain solutions of M$^*$-theory or Type II$^*$ background equations, as expected. Also starting with coboundary EDA's we provide examples of generalised Yang--Baxter deformations of M-theory and Type IIB backgrounds. The obtained results provide explicit examples when non-abelian U-duality works well as a solution generating transformation.

hep-th↗

arXiv2020

Polyvector deformations in eleven-dimensional supergravity

We consider 3- and 6-vector deformations of 11-dimensional supergravity backgrounds of the form $M_5\times M_6$ admitting at least 3 Killing vectors. Using flux formulation of the E${}_{6(6)}$ exceptional field theory we derive (sufficient) conditions for the deformations to generate a solution. In the group manifold case these generalisations of the classical Yang-Baxter equation for the case of r-matrices with 3 and 6 indices are shown to reproduce those obtained from exceptional Drinfeld algebra for E${}_{6(6)}$. In general we see an additional constraint, which might be related to higher exceptional Drinfeld algebras.

hep-th↗

arXiv2020

On non-abelian U-duality of 11D backgrounds

In this letter we generalised the procedure of non-abelian T-duality based on a B-shift and a sequence of formal abelian T-dualities in non-isometric directions to 11-dimensional backgrounds. This consists of a C-shift followed by either a formal U-duality transformation or taking a IIB section. We investigate restrictions and applicability of the procedure and find that it can provide supergravity solutions for the SL(5) exceptional Drinfeld algebra only when a spectator field is present, which is consistent with examples known in the literature.

hep-th↗

arXiv2020

Non-abelian tri-vector deformations in d=11 supergravity

A truncation of the SL(5) Exceptional Field Theory that allows to describe spacetimes of the form $M_4 \times M_7$ with the 4-form flux on $M_4$ is constructed. The resulting theory is used to test the recently proposed tri-vector generalisation of Yang-Baxter deformations applied to the AdS${}_4 \times \mathbb{S}^7$ solution in $d=11$ supergravity. We present two new supergravity solutions corresponding to non-abelian non-unimodular tri-vector deformations of AdS${}_4 \times \mathbb{S}^7$.

hep-th↗

arXiv2019

The different faces of branes in Double Field Theory

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.

hep-th↗

arXiv2019

Gauge field fluxes and Bianchi identities in extended field theories

Tensor hierarchy of Exceptional Field Theories contains gauge fields satisfying certain Bianchi identities with source part governing interaction with standard and exotic branes. These are responsible for tadpole cancellation in compactification schemes and provide consistency constraints for cosmological model building. Analysis of reduction of (10+10)-dimensional DFT into (D+d+d)-dimensional split DFT allows to consider all Bianchi identities of the theory in the form analogous to the ExFT approach. Here we review in details and elaborate on these ideas.

hep-th↗

arXiv2019

Tri-vector deformations in $d=11$ supergravity

We construct a $d=11$ supergravity analogue of the open-closed string map in the context of SL(5) Exceptional Field Theory (ExFT). The deformation parameter tri-vector $Ω$ generalizes the non-commutativity bi-vector parameter $Θ$ of the open string. When applied to solutions in $d=11$, this map provides an economical way of performing TsT deformations, and may be used to recover $d=10$ Yang-Baxter deformations after dimensional reduction. We present a generalization of the Classical Yang-Baxter Equation (CYBE) for rank 3 objects, which emerges from $d=11$ supergravity and the SL(5) ExFT. This equation is shown to reduce to the $d=10$ CYBE upon dimensional reduction.

hep-th↗

arXiv2019

Dynamics of branes in Double Field Theory

In this contribution the construction of the Wess-Zumino term for Dp-branes and NS 5-branes invariant under T-duality is described. The cases of the massless Type IIA/B and the massive Type IIA theories are covered. Mass parameter is introduced by generalized Scherk-Schwarz ansatz of O(10,10) spinor and tensor fields. The results lead to the picture where a given brane is understood as an invariant object rotated into the full doubled space.

hep-th↗

arXiv2019

Exotic Branes in M-Theory

We revisit curious objects in string and M-theory called exotic brane---objects that are highly non-perturbative, possessing a tension that scales less than $g_s^{-2}$ and are generically of low-codimension. They are non-geometric in the sense that they are only well-defined locally as supergravity solutions and require duality transformations to patch correctly, in addition to the usual diffeomorphisms and gauge transformations. We argue that Double Field Theory (DFT) and Exceptional Field Theory (EFT) are the prime setting in which to examine such objects. To emphasise this, we construct an explicit solution in $E_{7(7)} \times \mathbb{R}^+$ EFT that unifies many of the codimension-2 exotic branes into a single well-behaved solution on an extended spacetime. We further argue that there are in fact an infinite number of exotic branes in string- and M-theory, many of which fall into a more general class of exotic branes that do not afford even a local description in terms of conventional supergravity.

hep-th↗

arXiv2018

T-duality and entanglement entropy for NS five-branes

In this work an algorithm is proposed to calculate entropy for field theories living on NS five branes, which gives a result invariant under T-duality. This is a deformation of the well known Ryu-Takayanagi formula, which takes into account dependence of localized backgrounds for the branes on winding modes of strings.

hep-th↗

arXiv2018

Exotic Branes in Exceptional Field Theory: $E_{7(7)}$ and Beyond

In recent years, it has been widely argued that the duality transformations of string and M-theory naturally imply the existence of so-called `exotic branes'---low codimension objects with highly non-perturbative tensions, scaling as $g_s^α$ for $α\leq -3$. We argue that their intimate link with these duality transformations make them an ideal object of study using the general framework of Double Field Theory (DFT) and Exceptional Field Theory (EFT)---collectively referred to as ExFT. Parallel to the theme of dualities, we also stress that these theories unify known solutions in string- and M-theory into a single solution under ExFT. We argue that not only is there a natural unifying description of the lowest codimension objects, many of these exotic states require this formalism as a consistent supergravity description does not exist.

hep-th↗

arXiv2018

Five-brane actions in double field theory

We construct an action for NSNS 5-branes which is manifestly covariant under O(d,d). This is done by doubling $d$ of the spacetime coordinates which appear in the worldvolume action. By formulating the DBI part of the action in a manner similar to a "gauged sigma model", only half the doubled coordinates genuinely appear. Our approach allows one to describe the full T-duality orbit of the IIB NS5 brane, the IIA KKM and their exotic relations in one formalism. Furthermore, by using ideas from double field theory, our action can be said to describe various aspects of non-geometric five-branes.

hep-th↗

arXiv2017

Integrability properties of Motzkin polynomials

We consider a Hamiltonian system which has its origin in a generalization of exact renormalization group flow of matrix scalar field theory and describes a non-linear generalization of the shock-wave equation that is known to be integrable. Analyzing conserved currents of the system the letter shows, that these follow a nice pattern governed by coefficients of Motzkin polynomials, where each integral of motion corresponds to a path on a unit lattice.

hep-th↗

arXiv2017

O(d+1,d+1) enhanced double field theory

Double field theory yields a formulation of the low-energy effective action of bosonic string theory and half-maximal supergravities that is covariant under the T-duality group O$(d,d)$ emerging on a torus $T^d$. Upon reduction to three spacetime dimensions and dualisation of vector fields into scalars, the symmetry group is enhanced to O$(d+1,d+1)$. We construct an enhanced double field theory with internal coordinates in the adjoint representation of O$(d+1,d+1)$. Its section constraints admit two inequivalent solutions, encoding in particular the embedding of $D=6$ chiral and non-chiral theories, respectively. As an application we define consistent generalized Scherk-Schwarz reductions using a novel notion of generalized parallelization. This allows us to prove the consistency of the truncations of $D=6$, ${\cal N}=(1,1)$ and $D=6$, ${\cal N}=(2,0)$ supergravity on AdS$_3\times \mathbb{S}^3$.

hep-th↗

arXiv2016

Non-geometric branes are DFT monopoles

The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known $5^2_2$ solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic charge of (unsmeared) NS5-brane.

hep-th↗

arXiv2015

Unified phonon-based approach to the thermodynamics of solid, liquid and gas states

We introduce a unified approach to states of matter (solid, liquid and gas) and describe the thermodynamics of the pressure-temperature phase diagram in terms of phonon excitations. We derive the effective Hamiltonian with low-energy cutoff in two transverse phonon polarizations (phononic band gaps) by breaking the symmetry in phonon interactions. Further, we construct the statistical mechanics of states of aggregation employing the Debye approximation. The introduced formalism covers the Debye theory of solids, the phonon theory of liquids, and thermodynamic limits such as the Dulong-Petit thermodynamic limit, the ideal gas limit and the new thermodynamic limit, dubbed here the Frenkel line thermodynamic limit. We discuss the phonon propagation and localization effects in liquids above and below the Frenkel line, and explain the "fast sound" phenomenon. As a test for our theory we calculate velocity-velocity autocorrelation and pair distribution functions within the Green-Kubo formalism. We show the consistency between dynamics of phonons and pair correlations in the framework of the unified approach. New directions towards advancements in phononic band gaps engineering, hypersound manipulation technologies and exploration of exotic behaviour of fluids relevant to geo- and planetary sciences are discussed. The presented results are equally important both for practical implications and for fundamental research.

cond-mat.stat-mech↗

arXiv2015

Exceptional field theory: $SL(5)$

In this work the exceptional field theory formulation of supergravity with SL(5) gauge group is considered. This group appears as a U-duality group of $D=7$ maximal supergravity. In the formalism presented the hidden global duality group is promoted into a gauge group of a theory in dimensions 7+number of extended directions. This work is a continuation of the series of works for $E_{8,7,6}, SO(5,5)$ and $SL(3)\times SL(2)$ duality groups.

hep-th↗

arXiv2015

Exceptional field theory: $SO(5,5)$

We construct Exceptional Field Theory for the group $SO(5,5)$ based on the extended (6+16)-dimensional spacetime, which after reduction gives the maximal $D=6$ supergravity. We present both a true action and a duality-invariant pseudo-action formulations. All the fields of the theory depend on the complete extended spacetime. The U-duality group $SO(5,5)$ is made a geometric symmetry of the theory by virtue of introducing the generalised Lie derivative that incorporates a local duality transformation. Tensor hierarchy appears as a natural consequence of the algebra of generalised Lie derivatives that are viewed as gauge transformations. Upon truncating different subsets of the extra coordinates, maximal supergravities in $D=11$ and $D=10$ (type IIB) can be recovered from this theory.

hep-th↗