D3+D6 solution and D4+D6 solution

We make the supergravity solutions describing the branes (D3 branes and D4 branes) localized within the D6 branes in the near core region of D6 brane. From the D=11 solutions (M3 branes and M4 branes with the Z_N identifications in the transverse space) we obtain the D=10 supergravity solutions of D3 branes localized within D6 branes and D4 branes localized within D6 branes by reducing the dimension down to D=10 along a circular direction of S³ part of the transverse space. M3 brane solution leads to D=10 background representing D3 branes localized on D6 branes in the region close to the D6 branes core. M4 branes lead to the D4 branes localized on D6 branes in the region close to the D6 brane core.     

Kähler metrics and gauge kinetic functions for intersecting D6‐branes on toroidal orbifolds – The complete perturbative story

We systematically derive the perturbatively exact holomorphic gauge kinetic function, the open string Kähler metrics and closed string Kähler potential on intersecting D6‐branes by matching open string one‐loop computations of gauge thresholds with field theoretical gauge couplings in 𝒩 = 1 supergravity. We consider all cases of bulk, fractional and rigid D6‐branes on T⁶/Ω ℛ and the orbifolds T⁶/(ℤ_N × Ω ℛ) and T⁶/(ℤ₂ × ℤ_2M × Ω ℛ) without and with discrete torsion, which differ in the number of bulk complex structures and in the bulk Kähler potential. Our analysis includes all supersymmetric configurations of vanishing and non‐vanishing angles among D6‐branes and O6‐planes, and all possible Wilson line and displacement moduli are taken into account. The shape of the Kähler moduli turns out to be orbifold independent but angle dependent, whereas the holomorphic gauge kinetic functions obtain three different kinds of one‐loop corrections: a Kähler moduli dependent one for some vanishing angle independently of the orbifold background, another one depending on complex structure moduli only for fractional and rigid D6‐branes, and finally a constant term from intersections with O6‐planes. These results are of essential importance for the construction of the related effective field theory of phenomenologically appealing D‐brane models. As first examples, we compute the complete perturbative gauge kinetic functions and Kähler metrics for some T⁶/ℤ₂ × ℤ₂ examples with rigid D‐branes of [1]. As a second class of examples, the Kähler metrics and gauge kinetic functions for the fractional QCD and leptonic D6‐brane stacks of the Standard Model on T⁶/ℤ₆^′T⁶/ℤ₆^′ from [2] are given.     

The self-dual string soliton in AdS<Subscript>4</Subscript>×S<Superscript>7</Superscript> spacetime

We construct self-dual string soliton solutions in AdS₄×S⁷ spacetime, starting from the covariant equations of motion of the M5-brane. We study the properties of the solutions and find that their actions are linearized, indicating the BPS nature of the solutions, and we find that they have the same electric and magnetic charges. The straight string soliton solution represents the configuration of the membranes ending on a M5-brane with a straight string intersection, and it behaves like the spiky solution in flat spacetime. The spherical string soliton solution, which could be related to the straight one by a conformal transformation, represents the membranes ending on a M5-brane with a spherical intersection.     

Review of AdS/CFT Integrability, Chapter II.1: Classical AdS 5 × S 5 String Solutions

We review basic examples of classical string solutions in AdS ₅?× S ⁵. We concentrate on simplest rigid closed string solutions of circular or folded type described by integrable 1-d Neumann system but mention also various generalizations and related open-string solutions.     

On the classical dynamics of a pure spinor string on an AdS5×S5 background

We will discuss some properties of the pure spinor string on an AdS₅×S⁵ background. Using a classical Hamiltonian analysis we will show that the vertex operator for the massless state that is in the cohomology of the BRST charges describes on-shell fluctuations around an AdS₅×S⁵ background.     

Quadratic corrections to three‐point functions

Following the recent progress on the calculation of three‐point correlators with two “heavy” (with large quantum numbers) and one “light” states at strong coupling, we compute the logarithmic divergent terms of leading bosonic quantum corrections to correlation functions with “heavy” operators corresponding to simple string solutions in AdS₅ × S⁵. The “light” operator is chosen to be the dilaton. An important relation connecting the corrections to both the dimensions of “heavy” states, and the structure constants is recovered.     

Electric/magnetic deformations of S3 and AdS3, and geometric cosets

We analyze asymmetric marginal deformations of SU(2)_k and SL(2,ℝ)_k WZW models. These appear in heterotic string backgrounds with non‐vanishing Neveu–Schwarz three‐forms plus electric or magnetic fields, depending on whether the deformation is elliptic, hyperbolic or parabolic. Asymmetric deformations create new families of exact string vacua. The geometries which are generated in this way, deformed S³ or AdS₃, include in particular geometric cosets such as S², AdS₂ or H₂. Hence, the latter are consistent, exact conformal sigma models, with electric or magnetic backgrounds. We discuss various geometric and symmetry properties of the deformations at hand as well as their spectra and partition functions, with special attention to the supersymmetric AdS₂ × S² background. We also comment on potential holographic applications.     

Intersectingp — p′ branes inpp-wave background

Several supergravity solutions corresponding to bothDp, as well asDp—Dp′ systems, inNS-NS andR-R pp-wave background originating fromAdS ₃ xS ³ xR ⁴ are presented. The supersymmetry properties of these solutions are analysed along with a brief outline of the world sheet construction for thep — p′ branes.     

The Bethe ansatz equations for reflecting magnons

We derive the Bethe ansatz equations on the half line for particles interacting through factorized S-matrices invariant relative to the centrally extended su(2|2) Lie superalgebra and su(1|2) open boundaries. These equations may be of relevance for the study of the spectrum of open strings on AdS₅×S⁵ background attached to Y=0 giant graviton branes. A one-dimensional spin chain Hamiltonian associated to this system is also derived.     

Review of AdS/CFT Integrability,Chapter II.2: Quantum Strings in AdS<Subscript>5</Subscript> × S<Superscript>5</Superscript>

We review the semiclassical analysis of strings in AdS₅ × S⁵ with a focus on the relationship to the underlying integrable structures. We discuss the perturbative calculation of energies for strings with large charges, using the folded string spinning in AdS₃ ? AdS₅ as our main example. Furthermore, we review the perturbative light-cone quantisation of the string theory and the calculation of the worldsheet S-matrix.     

{\mathcal{N} = 2} Supersymmetric AdS4 Solutions of M-theory

We analyse the most general ${\mathcal{N} = 2}$ supersymmetric solutions of D = 11 supergravity consisting of a warped product of four-dimensional anti-de-Sitter space with a seven-dimensional Riemannian manifold Y ₇. We show that the necessary and sufficient conditions for supersymmetry can be phrased in terms of a local SU(2)-structure on Y ₇. Solutions with non-zero M2-brane charge also admit a canonical contact structure, in terms of which many physical quantities can be expressed, including the free energy and the scaling dimensions of operators dual to supersymmetric wrapped M5-branes. We show that a special class of solutions is singled out by imposing an additional symmetry, for which the problem reduces to solving a second order non-linear ODE. As well as recovering a known class of solutions, that includes the IR fixed point of a mass deformation of the ABJM theory, we also find new solutions which are dual to cubic deformations. In particular, we find a new supersymmetric warped AdS₄ × S ⁷ solution with non-trivial four-form flux.     

The Integral Form of D = 3 Chern‐Simons Theories Probing Singularities

We consider D=3 supersymmetric Chern Simons gauge theories both from the point of view of their formal structure and of their applications to the AdS₄/CFT₃ correspondence. From the structural view‐point, we use the new formalism of integral forms in superspace that utilizes the rheonomic Lagrangians and the Picture Changing Operators, as an algorithmic tool providing the connection between different approaches to supersymmetric theories. We provide here the generalization to an arbitrary Kähler manifold with arbitrary gauge group and arbitrary superpotential of the rheonomic lagrangian of D=3 matter coupled gauge theories constructed years ago. From the point of view of the AdS₄/CFT₃ correspondence and more generally of M2‐branes we emphasize the role of the Kähler quotient data in determining the field content and the interactions of the Cherns Simons gauge theory when the transverse space to the brane is a non‐compact Kähler quotient K ₄ of some flat variety with respect to a suitable group. The crepant resolutions of singularities fall in this category. In the present paper we anticipate the general scheme how the geometrical data are to be utilized in the construction of the D=3 Chern‐Simons Theory supposedly dual to the corresponding M2‐brane solution.     

An SL(2,ℝ)‐covariant,first order, κ‐supersymmetric action for the D5‐brane

The new first order, rheonomic, κ–supersymmetric formalism recently introduced by us for the world‐volume action of the D3 brane is extended to the case of D5 branes. This extension requires the dual formulation of the Free Differential Algebra of type IIB supergravity in terms of 6–form gauge potentials which was so far missing and is given here. Furthermore relying on our new approach we are able to write the D5 world volume action in a manifestly SL(2,ℝ) covariant form. This is important in order to solve the outstanding problem of finding the appropriate boundary actions of D3–branes on smooth ALE manifolds with twisted fields. The application of our results to this problem is however postponed to a subsequent publication.     

Wilson loops in 3<Emphasis Type="Italic">d</Emphasis> QFT from D-branes in AdS<Subscript>4</Subscript>×CP<Superscript>3</Superscript>

We study the Wilson loops in three-dimensional QFT from the D-branes in the AdS₄×CP³ geometry. We find explicit D-brane configurations in the bulk which correspond to both straight and circular Wilson lines extended to the boundary of AdS₄. We analyze critically the role of boundary contributions to the D2-branes with various topology and fundamental string actions.     

On the M5 and the AdS 7/CFT 6 correspondence

The chiral primary operators of the D=6 superconformal (2,0) theory corresponding to 14 scalars of N=4 D=7 supergravity are obtained by expanding the world volume action for the M5-brane around an AdS ₇×S ⁴ background. In the leading order, the operators take their values in the symmetric traceless representation of the SO(5) R-symmetry group in consistency with the early conjecture on their structure based on the superconformal symmetry and Matrix-like model arguments.     

A Geometric Construction of the Exceptional Lie Algebras <Emphasis Type="Italic">F</Emphasis><Subscript>4</Subscript> and <Emphasis Type="Italic">E</Emphasis><Subscript>8</Subscript>

We present a geometric construction of the exceptional Lie algebras F ₄ and E ₈ starting from the round spheres S ⁸ and S ¹⁵, respectively, inspired by the construction of the Killing superalgebra of a supersymmetric supergravity background.