We discuss dual formulations of D-brane intersections. The duality is between world volume field theories of different dimensionalities which both describe the same D-brane configuration but are valid in complementary regions of parameter space. We discuss the duality in terms of bion configurations involving D-strings orthogonally intersecting both D3-branes and D5branes. Based on the talk presented by R. C. Myers at Strings 2001, Bombay, India E-mail: constabl@hep.physics.mcgill.ca E-mail: rcm@hep.physics.mcgill.ca E-mail: tafjord@physics.mcgill.ca

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)xS(1) slice of AdS(5)xS(5). We consider the AdS/CFT dictionary for this setup. In particular we find classical probe fluctuations corresponding to the holomorphic curve wy=calpha('). These fluctuations are dual to defect fields containing massless two-dimensional scalars which parametrize 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 nonrenormalization theorem is conjectured for the correlators of these operators, and verified to order g(2).

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 (dCFT) with two-dimensional (4,0) supersymmetry. This defect CFT describes the low-energy theory of intersecting D3-branes at a ${C}^{2}/{Z}_{k}$ orbifold. In an appropriate $\stackrel{\ensuremath{\rightarrow}}{k}\ensuremath{\infty}$ limit, two compact spatial directions are generated. By identifying moduli of the M5-M5 intersection in terms of those of the defect CFT, we argue that the ${\mathrm{SU}(2)}_{L}R$ symmetry of the (4,0) defect CFT matches the $\mathrm{SU}(2)R$ symmetry of the $\mathcal{N}=2,d=4$ theory of the M5-M5 intersection. We find a 't Hooft anomaly in the ${\mathrm{SU}(2)}_{L}R$ symmetry, suggesting that tensionless strings give rise to an anomaly in the $\mathrm{SU}(2)R$ symmetry of intersecting M5-branes.

We express all correlation functions in timelike boundary Liouville theory as unitary matrix integrals and develop efficient techniques to evaluate these integrals. We compute large classes of correlation functions explicitly, including an infinite number of terms in the boundary state of the rolling tachyon. The matrix integrals arising here also determine the correlation functions of gauge invariant operators in two dimensional Yang-Mills theory, suggesting an equivalence between the rolling tachyon and QCD(2).

The defect conformal field theory describing intersecting D3‐branes at a \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ \mathbb{C}^2 / \mathbb{Z}_k $\end{document} sorbifold is used to deconstruct the theory of intersecting M5‐branes, as well as M5‐branes wrapping the holomorphic curve xy = c . The possibility of a 't Hooft anomaly due to tensionless strings at the intersection is discussed.

We study a defect conformal field theory describing D3-branes intersecting over two spacetime dimensions. This theory admits an exact Lagrangian description which includes both twoand four-dimensional degrees of freedom, has (4, 4) supersymmetry and is invariant under global conformal transformations. Both twoand 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 AdS3×S slice of AdS5×S. We consider the AdS/CFT dictionary for this set-up. In particular we find classical probe fluctuations corresponding to the holomorphic curve wy = cα′. 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 g2. ∗constabl@lns.mit.edu, jke@physik.hu-berlin.de, zack@physik.hu-berlin.de, ik@physik.hu-berlin.de

Recently, Berenstein et al. have proposed a duality between a sector of = 4 super-Yang-Mills theory with large R-charge J, and string theory in a pp-wave background. In the limit considered, the effective 't Hooft coupling has been argued to be ?' = gYM2N/J2 = 1/(?p+?')2. We study Yang-Mills theory at small ?' (large ?) with a view to reproducing string interactions. We demonstrate that the effective genus counting parameter of the Yang-Mills theory is g22 = J4/N2 = (4?gs)2(?p+?')4, the effective two-dimensional Newton constant for strings propagating on the pp-wave background. We identify g2(?')1/2 as the effective coupling between a wide class of excited string states on the pp-wave background. We compute the anomalous dimensions of BMN operators at first order in g22 and ?' and interpret our result as the genus one mass renormalization of the corresponding string state. We postulate a relation between the three-string vertex function and the gauge theory three-point function and compare our proposal to string field theory. We utilize this proposal, together with quantum mechanical perturbation theory, to recompute the genus one energy shift of string states, and find precise agreement with our gauge theory computation.

In this note we update the discussion of the BMN correspondence and string interactions in hep-th/0205089 to incorporate the effects of operator mixing. We diagonalize the matrix of two point functions of single and double trace operators, and compute the eigen-operators and their anomalous dimensions to order g_2^2 \lambda'. Surprisingly, operators in different R symmetry multiplets remain degenerate at this order. We also calculate the corresponding energy shifts in string theory, and find a discrepancy with field theory results, indicating possible new effects in light-cone string field theory.

We study a generalization of the Randall-Sundrum mechanism for generating the weak/Planck hierarchy, which uses two rather than one warped extra dimension, and which requires no negative tension branes. A 4-brane with one exponentially large compact dimension plays the role of the Planck brane. We investigate the dynamical stability with respect to graviton, graviphoton and radion modes. The radion is shown to have a tachyonic instability for certain models of the 4-brane stress-energy, while it is stable in others, and massless in a special case. If stable, its mass is in the milli-eV range, for parameters of the model which solve the hierarchy problem. The radion is shown to couple to matter with gravitational strength, so that it is potentially detectable by submillimeter-range gravity experiments. The radion mass can be increased using a bulk scalar field in the manner of Goldberger and Wise, but only to order MeV, due to the effect of the large extra dimension. The model predicts a natural scale of 10^{13} GeV on the 4-brane, making it a natural setting for inflation from the ultraviolet brane.

We present new non-Abelian solitonic configurations in the low energy effective theory describing a collection of N parallel D1--branes. These configurations preserve 1/4, 1/8, 1/16 and 1/32 of the spacetime supersymmetry. They are solutions to a set of generalised Nahm's equations which are related to self-duality equations in eight dimensions. Our solutions represent D1--branes which expand into fuzzy funnel configurations ending on collections of intersecting D3--branes. Supersymmetry dictates that such intersecting D3--branes must lie on a calibrated three-surface of spacetime and we argue that the generalised Nahm's equations encode the data for the construction of magnetic monopoles on the relevant three-surfaces.

We study a generalization of the Randall‐Sundrum mechanism for generating the weak/Planck hierarchy, which uses two rather one warped extra dimension, and which requires no negative tension brane. The dynamical stability of the Radion mode will be studied. It is shown to have a tachyonic instability for certain models of the 4‐brane stress energy, while stable or massless in other models. If stable, its mass is in the milli‐eV range. The issue of the Radion stabilizationby a bulk scalar field is investigated.

We consider the physics of enhancons as applied to four dimensional black holes which are constructed by wrapping both D-branes and NS-branes on K3. As was recently shown for the five dimensional black holes, the enhancon is crucial in maintaining consistency with the second law of thermodynamics. This is true for both the D-brane and NS-brane sectors of these black holes. In particular NS5-branes in both type IIA and IIB string theory are found to exhibit enhancon physics when wrapped on a K3 manifold.

We discuss dual formulations of D-brane intersections. The duality is between world volume field theories of different dimensionalities which both describe the same D-brane configuration but are valid in complementary regions of parameter space. We discuss the duality in terms of bion configurations involving D-strings orthogonally intersecting both D3-branes and D5-branes.

We study new solutions of the low-energy equations of motion for the non-abelian D-string. We find a "fuzzy funnel" solution consisting of a noncommutative four-sphere geometry which expands along the length of the D-string. We show that this funnel solution has an interpretation as D-strings ending on a set of orthogonal D5-branes. Although not supersymmetric, the system appears to be stable within this framework. We also give a dual description of this configuration as a bion spike in the non-abelian world volume theory of coincident D5-branes.

We reconsider the four dimensional extremal black hole constructed in type-IIB string theory as the bound state of D1-branes, D5-branes, momentum, and Kaluza-Klein monopoles. Specifically, we examine the case of an arbitrary number of monopoles. Consequently, the weak coupling calculation of the microscopic entropy requires a study of the D1-D5 system on an ALE space. We find that the complete expression for the Bekenstein-Hawking entropy is obtained by taking into account the massless open strings stretched between the fractional D-branes which arise in the orbifold limit of the ALE space. The black hole sector therefore arises as a mixed Higgs-Coulomb branch of an effective 1 + 1 dimensional gauge theory.

We examine noncommutative solutions of the non-Abelian theory on the world-volume of N coincident D-strings. These solutions can be interpreted in terms of noncommutative geometry as funnels describing the non-Abelian D-string expanding out into an orthogonal D3-brane. These configurations are "dual" to the bion solutions in the Abelian world-volume theory of the D3-brane. In the latter, a charge N magnetic monopole describes N D-strings attached to the D3-brane with a spike deformation of the world volume. The noncommutative D-string solutions give a reliable account of physics at the core of the monopole, where the bion description is expected to break down. In the large N limit, we find good agreement between the two points of view, including the energy, couplings to background fields, and the shape of the funnel. We also study fluctuations traveling along the D-string, again obtaining agreement in the large N limit. At finite N, our results give a limit on the number of modes that can travel to infinity along the N D-strings attached to the D3-brane.