N=1,2 supersymmetric vacua of IIA supergravity and SU(2) structures

We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_{\omega} X_6$, where $X_6$ is a six-dimensional compact manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.Comment: 24 pages; v2: reference adde

Supersymmetric non-linear sigma-models with boundaries revisited

We study two-dimensional supersymmetric non-linear sigma-models with boundaries. We derive the most general family of boundary conditions in the non-supersymmetric case. Next we show that no further conditions arise when passing to the N=1 model. We present a manifest N=1 off-shell formulation. The analysis is greatly simplified compared to previous studies and there is no need to introduce non-local superspaces nor to go (partially) on-shell. Whether or not torsion is present does not modify the discussion. Subsequently, we determine under which conditions a second supersymmetry exists. As for the case without boundaries, two covariantly constant complex structures are needed. However, because of the presence of the boundary, one gets expressed in terms of the other one and the remainder of the geometric data. Finally we recast some of our results in N=2 superspace and discuss applications.Comment: LaTeX, 23 page

An index for the Dirac operator on D3 branes with background fluxes

We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type IIB string theory. To this end, we derive the Dirac equation on a Euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.Comment: Fermion coupling to five-form restored, conclusions of the paper unchange

The Worldvolume Action of Kink Solitons in AdS Spacetime

A formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit "kink" solution of a real scalar field in AdS spacetime is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in two expansion parameters--associated with the hypersurface fluctuation length and the radius of AdS spacetime respectively. Two alternative methods are given for doing this. The results are expressed in terms of the trace of the extrinsic curvature and the intrinsic scalar curvature. In addition to conformal Galileon interactions, we find a non-Galileon term which is never sub-dominant. This method can be extended to any conformally flat bulk spacetime.Comment: 32 pages, 3 figures, typos corrected and additional comments adde

(De)constructing Intersecting M5-branes

We describe intersecting M5-branes, as well as M5-branes wrapping the holomorphic curve xy=c, in terms of a limit of a defect conformal field theory with two-dimensional (4,0) supersymmetry. This dCFT describes the low-energy theory of intersecting D3-branes at a C^2/Z_k orbifold. In an appropriate k -> infinity limit, two compact spatial directions are generated. By identifying moduli of the M5-M5 intersection in terms of those of the dCFT, we argue that the SU(2)_L R-symmetry of the (4,0) defect CFT matches the SU(2) R-symmetry of the N =2, d=4 theory of the M5-M5 intersection. We find a 't Hooft anomaly in the SU(2)_L R-symmetry, suggesting that tensionless strings give rise to an anomaly in the SU(2) R-symmetry of intersecting M5-branes.Comment: latex, 25 pages, 4 figure

Supersymmetry and Branes in M-theory Plane-waves

We study brane embeddings in M-theory plane-waves and their supersymmetry. The relation with branes in AdS backgrounds via the Penrose limit is also explored. Longitudinal planar branes are originated from AdS branes while giant gravitons of AdS spaces become spherical branes which are realized as fuzzy spheres in the massive matrix theory.Comment: 17 pages, JHEP style, references added, typos correcte

Fermions and Type IIB Supergravity On Squashed Sasaki-Einstein Manifolds

We discuss the dimensional reduction of fermionic modes in a recently found class of consistent truncations of type IIB supergravity compactified on squashed five-dimensional Sasaki-Einstein manifolds. We derive the lower dimensional equations of motion and effective action, and comment on the supersymmetry of the resulting theory, which is consistent with N=4 gauged supergravity in $d=5$, coupled to two vector multiplets. We compute fermion masses by linearizing around two $AdS_{5}$ vacua of the theory: one that breaks N=4 down to N=2 spontaneously, and a second one which preserves no supersymmetries. The truncations under consideration are noteworthy in that they retain massive modes which are charged under a U(1) subgroup of the $R$-symmetry, a feature that makes them interesting for applications to condensed matter phenomena via gauge/gravity duality. In this light, as an application of our general results we exhibit the coupling of the fermions to the type IIB holographic superconductor, and find a consistent further truncation of the fermion sector that retains a single spin-1/2 mode.Comment: 43 pages, 2 figures, PDFLaTeX; v2: added references, typos corrected, minor change

String Theoretic Bounds on Lorentz-Violating Warped Compactification

We consider warped compactifications that solve the 10 dimensional supergravity equations of motion at a point, stabilize the position of a D3-brane world, and admit a warp factor that violates Lorentz invariance along the brane. This gives a string embedding of ``asymmetrically warped'' models which we use to calculate stringy (\alpha') corrections to standard model dispersion relations, paying attention to the maximum speeds for different particles. We find, from the dispersion relations, limits on gravitational Lorentz violation in these models, improving on current limits on the speed of graviton propagation, including those derived from field theoretic loops. We comment on the viability of models that use asymmetric warping for self-tuning of the brane cosmological constant.Comment: 20pg, JHEP3; v2 additional references, slight change to intro; v3. added referenc

Intersecting D3-branes and Holography

We study a defect conformal field theory describing D3-branes intersecting over two space-time dimensions. This theory admits an exact Lagrangian description which includes both two- and four-dimensional degrees of freedom, has (4,4) supersymmetry and is invariant under global conformal transformations. Both two- and four-dimensional contributions to the action are conveniently obtained in a two-dimensional (2,2) superspace. In a suitable limit, the theory has a dual description in terms of a probe D3-brane wrapping an AdS_3 x S^1 slice of AdS_5 x S^5. We consider the AdS/CFT dictionary for this set-up. In particular we find classical probe fluctuations corresponding to the holomorphic curve wy=c\alpha^{\prime}. These fluctuations are dual to defect fields containing massless two-dimensional scalars which parameterize the classical Higgs branch, but do not correspond to states in the Hilbert space of the CFT. We also identify probe fluctuations which are dual to BPS superconformal primary operators and to their descendants. A non-renormalization theorem is conjectured for the correlators of these operators, and verified to order g^2.Comment: 46 pages, 5 figures, Latex, minor corrections to section 4.2, version published in Phys. Rev.

Integrability in QCD and beyond

Yang--Mills theories in four space-time dimensions possess a hidden symmetry which does not exhibit itself as a symmetry of classical Lagrangians but is only revealed on the quantum level. It turns out that the effective Yang--Mills dynamics in several important limits is described by completely integrable systems that prove to be related to the celebrated Heisenberg spin chain and its generalizations. In this review we explain the general phenomenon of complete integrability and its realization in several different situations. As a prime example, we consider in some detail the scale dependence of composite (Wilson) operators in QCD and super-Yang--Mills (SYM) theories. High-energy (Regge) behavior of scattering amplitudes in QCD is also discussed and provides one with another realization of the same phenomenon that differs, however, from the first example in essential details. As the third example, we address the low-energy effective action in a N=2 SYM theory which, contrary to the previous two cases, corresponds to a classical integrable model. Finally, we include a short overview of recent attempts to use gauge/string duality in order to relate integrability of Yang--Mills dynamics with the hidden symmetry of a string theory on a curved background.Comment: 87 pages, 4 figures; minor stylistic changes, references added. To be published in the memorial volume 'From Fields to Strings: Circumnavigating Theoretical Phyiscs', World Scientific, 2004. Dedicated to the memory of Ian Koga