A new class is introduced of M2-branes solutions of d=11 supergravity that include internal fluxes obeying Englert equation in 7-dimensions. A simple criterion for the existence of Killing spinors in such backgrounds is established. Englert equation is viewed as the generalization to d=7 of Beltrami equation defined in d=3 and it is treated accordingly. All 2-brane solutions of minimal d=7 supergracity can be uplifted to d=11 and have supersymmetry. It is shown that the simple group PSL(2, 7) is crystallographic in d=7 having an integral action on the A7 root lattice. By means of this point-group and of the T^{7} torus obtained quotiening with the A7 root lattice we were able to construct new M2 branes with Englert fluxes and . In particular we exhibit here an solution depending on 4-parameters and admitting a large non abelian discrete symmetry, namely . The dual field theories have the same symmetries and have complicated non linear interactions.

Gauge coupling unification is studied within the framework where there are extra Higgs doublets and *E*_{6} exotic fields. Supersymmetric models and nonsupersymmetric models are investigated, and a catalog of models with gauge coupling unification is presented.

In this paper we consider entanglement entropies in two-dimensional conformal field theories in the presence of topological interfaces. Tracing over one side of the interface, the leading term of the entropy remains unchanged. The interface however adds a subleading contribution, which can be interpreted as a relative (Kullback-Leibler) entropy with respect to the situation with no defect inserted. Reinterpreting boundaries as topological interfaces of a chiral half of the full theory, we rederive the left/right entanglement entropy in analogy with the interface case. We discuss WZW models and toroidal bosonic theories as examples.

]]>The AdS/CFT correspondence, which holographically relates a gravitational theory in an anti-de Sitter (AdS) bulk space to a conformally field theory (CFT) on the AdS boundary, has led to many deep and new insights about the structure of gauge theories and about questions in quantum gravity and black holes. The cover picture of this year is showing a projection of an AdS space with a black hole in its interior. (Image on title page by Migael Strydom and Johanna Erdmenger)

This contribution collects background material and references for the overview talk that was delivered in the 21st European string workshop and 3rd COST MP1210 meeting, ‘The String Theory Universe’.

]]>We review the construction of a duality-invariant higher-derivative theory based on a doubled metric. This theory incorporates the corrections needed in the Green-Schwarz anomaly cancellation mechanism. We note recent progress in elucidating the structure of the theory. This article is largely based on the plenary talk given by B. Zwiebach at “The String Theory Universe”, 21st European String Workshop, Leuven, September 7-11, 2015.

]]>In this paper we review the appearance and utility of a nilpotent chiral multiplet in the context of supergravity, string theory and cosmology. Coupling a nilpotent chiral superfield to supergravity, one obtains what is called *pure dS supergravity*, a supergravity theory without scalar degrees of freedom that naturally has de Sitter (dS) solutions, and in which supersymmetry is non-linearly realized. We extend previous results that couple this dS supergravity to chiral and vector multiplets and derive the most general supergravity action for a single nilpotent chiral multiplet coupled to supergravity and an arbitrary number of chiral and vector multiplets. *Based in part on the plenary talk given by T. W. at “The String Theory Universe”, 21st European String Workshop, Leuven, September 7-11, 2015*.

We review some recent developments regarding supersymmetric field theories in six and five dimensions. In particular, we will describe the classification of supersymmetric six-dimensional theories with a holographic IIA dual; they are “linear quivers” consisting of chains of many SU (or SO/Sp) gauge groups connected by hypermultiplets and tensor multiplets. We will also describe the wider classification of supersymmetric six-dimensional theories that can be engineered in F-theory; these are also chains, but they include exceptional gauge groups and copies of a more exotic “E-string” theory with a single tensor and *E*_{8} flavor symmetry. Finally we discuss some properties of these theories under compactification to lower dimensions.

Supersymmetry-breaking is a key ingredient for string theory models to be phenomenologically viable. We review the strong analogy in the physics and methods used for describing non-supersymmetric flux vacua and non-supersymmetric black holes in string theory. We also show how the polarized state could be the key to describing a well-behaved back-reaction of anti-branes in flux backgrounds, shedding a new light on a recent debate in the literature.

]]>Magnetic impurities are responsible for many interesting phenomena in condensed matter systems, notably the Kondo effect and quantum phase transitions. Here we present a holographic model of a magnetic impurity that captures the main physical properties of the large-spin Kondo effect. We estimate the screening length of the Kondo cloud that forms around the impurity from a calculation of entanglement entropy and show that our results are consistent with the *g*-theorem.

Do electric/magnetic deformations of supergravity enjoy a string/M-theory origin, or are they just a four-dimensional artefact? We address this question for the gauging of a group closely related to : its contraction . We argue that the deformed supergravity arises from consistent truncation of massive IIA supergravity on *S*^{6}, and its electric/magnetic deformation parameter descends directly from the Romans mass. The critical points of the supergravity uplift to AdS_{4} massive type IIA vacua and the corresponding CFT_{3} duals are identified as super-Chern-Simons-matter theories with gauge group and level *k* given also by the Romans mass.

Defect Conformal Field Theories describe critical points of Quantum Field Theories excited or modified in the neighbourhood of a large *p*-dimensional submanifold. We elucidate the constraints of conformal invariance on correlation functions and we provide both recurrence relations, and in some cases exact results, for the conformal blocks with scalar external operators.

We briefly review the topic of AdS (in)stability, mainly focusing on a recently introduced analytic approach and its interplay with numerical results.

]]>In general three-dimensional conformal field theories (CFTs), the entanglement entropy receives a logarithmic contribution whenever the entangling surface contains a sharp corner of opening angle θ. Such contribution is controlled by a regulator-independent function which vanishes as in the smooth-surface limit (). We review our recent conjecture that for general three-dimensional CFTs, this corner coefficient σ is determined by *C*_{T}, the coefficient appearing in the two-point function of the stress tensor through the relation . We also comment on the extension of this conjecture to general Rényi entropies and higher-dimensional CFTs.

We review recent developments in the construction of integrable η- and λ-deformations of the superstring. We highlight their link with Poisson-Lie T-duality.

]]>This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II flux compactifications can be restated as integrability constraints on certain generalised complex structures. This reformulation uses generalised complex geometry, a mathematical framework that geometrizes the B-field. Secondly, we discuss how exceptional generalised geometry may provide a similar geometrization of the RR fields. Thirdly, we examine the connection between generalised geometry and non-geometry, and finally we present recent developments where generalised geometry is used to construct explicit examples of flux compactifications to flat space.

]]>The covariant and kappa–symmetric action for superstring in direct product of two flat , superspaces is constructed with the use of the PST formalism. It is manifestly T-duality invariant in the sense that the fields describing oscillating and winding modes enter it on equal footing.

]]>Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. This allows for the wave and monopole solutions to be combined into a single solution which obeys a twisted self-duality relation. All fundamental, solitonic and Dirichlet branes of ten- and eleven-dimensonal supergravity may be extracted from this single solution in Exceptional Field Theory.

]]>We discuss the four-dimensional massless spectrum of supersymmetric Minkowski compactifications of ten-dimensional heterotic supergravity, including the anomaly cancelation condition. This can be calculated from restrictions arising from F-term conditions in a four dimensional effective theory. The results agree with computations of the infinitesimal moduli space recently performed from a ten-dimensional perspective. The paper is based on a talk given by Eirik Eik Svanes in Leuven for the workshop on 'The String Theory Universe'.

]]>Branes at a singularity give rise to two different toric quiver gauge theories, which are related by Seiberg duality. We study where in the Kähler moduli space each of them is physically realized.

]]>Generalized geometry provides the framework for a systematic approach to non-symmetric metric gravity theory and naturally leads to an Einstein-Kalb-Ramond gravity theory with totally anti-symmetric contortion.

]]>In this contribution we describe dual higher–derivative formulations of some cosmological models based on supergravity. Work in this direction started with the Starobinsky model, whose supersymmetric extension was derived in the late 80's and was recently revived in view of new CMB data. Models dual to higher-derivative theories are subject to more restrictions than their bosonic counterparts or standard supergravity. The three sections are devoted to a brief description of supergravity, to a scale invariant *R*^{2} Supergravity and to theories with a nilpotent curvature, whose duals describe non-linear realizations (in the form of a Volkov–Akulov constrained superfield) coupled to supergravity.

We summarize the recent generalization of the Janis–Newman algorithm in view of its application to (gauged) supergravity. In particular this includes an extension of the algorithm to gauge fields and complex scalar fields, to topological horizons, to dyonic and NUT charges.

]]>Non-relativistic geometries have received more attention lately. We review our attempts to construct supersymmetric extensions of this so-called Newton–Cartan geometry in three space-time dimensions.

]]>Intersecting D6-branes provide a geometrically intuitive road to stringy particle physics models, where D6-branes stuck at orbifold singularities can lead to the stabilisation of deformation moduli, and the QCD axion can arise from the open string sector in a very constrained way compared to pure field theory. We demonstrate this interplay of different physical features here through an explicit model.

]]>We use exceptional field theory to establish a duality between certain consistent 7-dimensional truncations with maximal SUSY from IIA to IIB. We use this technique to obtain new consistent truncations of IIB on *S*^{3} and and also give a no-go theorem for the uplift of certain gaugings.

Soft behaviour of closed string amplitudes involving dilatons, gravitons and anti-symmetric tensors, is studied in the framework of bosonic string theory. The leading double soft limit of gluons is analysed as well, starting from scattering amplitudes computed in the open bosonic string. Field theory expressions are then obtained by sending the string tension to infinity. The presented results have been derived in the papers of Ref [1].

]]>We review the construction of six-dimensional non-geometric string compactifications obtained from torus fibrations with T-duality monodromy. We take a geometric point of view where T-duality twists are identified with Dehn twists of an auxiliary surface fibered over a two dimensional base. Degenerations of this auxiliary surface define codimension-two T-duality defects. For a large class of heterotic defects, we extract the low energy physics by constructing F-theory duals that admit simple Calabi-Yau resolutions.

]]>We remark that the two 10D massive deformations of the maximal type IIA supergravity (Romans and HLW supergravity) are associated to the low energy limit of the uplift to 10D of M2-brane torus bundles with parabolic monodromy linearly and non-linearly realized respectively. Romans supergravity corresponds to M2-brane compactified on a twice-punctured torus bundle.

]]>The curved space generalization of near-Hagedorn string thermodynamics is discussed in terms of the thermal scalar mode. This mode singly winds the compact time direction and represents the most dominating state near the Hagedorn temperature. We discuss the random walk picture in a curved background and its relation to the thermal scalar. Then we apply this formalism to the thermal gas near black hole horizons, where a long random walking string is found at string length from the black hole horizon, in agreement with Susskind's picture of the stretched membrane.

]]>The surface transport properties of stationary relativistic lumps of fluid are presented to first order in a derivative expansion based on an effective action approach. In the context of AdS/CFT, these lumps are known as plasma-balls and describe finite temperature configurations of compactified Super Yang Mills.

]]>We review the stabilisation of complex structure moduli in Type IIA orientifolds, especially on with discrete torsion, via deformations of orbifold singularities. While D6-branes in SO(2*N*) and USp(2*N*) models always preserve supersymmetry and thus give rise to flat directions, in an exemplary Pati-Salam model with only U(*N*) gauge groups ten out of the 15 deformation moduli can be stabilised at the orbifold point.

In this study the locally rotationally symmetric (LRS) Bianchi type-I (BI) cosmological model has been investigated in the presence of one dimensional cosmic strings in gravity. The exact solutions of the field equations are obtained through the use of constant deceleration parameter and the scalar expansion is proportional to the shear scalar. Considering the accelerating nature of the universe in the present epoch, the physical behavior of the model has been discussed.

]]>We construct global semi-realistic supersymmetric models with intersecting D6-branes on the non-factorisable orientifold . The non-factorisable structure gives rise to differences compared to the factorisable case: additional conditions for the three-cycles to be Lagrangian and extra constraints on the wrapping numbers for building fractional cycles.

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