Worldvolume Geometry Research Articles

On co-dimension 2 defect anomalies in N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM and (2,0) theory via brane probes in AdS/CFT

We consider a 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS solution for a D3 brane probe in AdS5× S5 that has world-volume geometry of AdS3× S1. It intersects the boundary over a surface that represents a dimension 2 defect in the boundary N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 SYM theory. The effective action of the probe brane is proportional to the logarithmically divergent volume of AdS3 and may thus be interpreted as computing conformal anomaly of supersymmetric S2 defect. The classical action scales as N. We compute the 1-loop correction to it due to quantum fluctuations of the D3 brane world-volume fields and compare the result to an earlier suggested expression for the defect anomaly. We also perform a similar analysis of a 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document}-BPS M5 brane probe solution in AdS7× S4 with the world-volume geometry of AdS5× S1 that represents a dimension 4 defect in the boundary (2,0) 6d theory. Here the classical M5 brane action computes the leading order N2 term in a-anomaly of the supersymmetric S4 defect. We perform a detailed computation of the 1-loop correction to the M5 brane effective action and thus provide a prediction for the subleading constant in the S4 defect a-anomaly coefficient.

Giant Wilson loops and AdS2/dCFT1

The 1/2-BPS Wilson loop in mathcal{N} = 4 supersymmetric Yang-Mills theory is an important and well-studied example of conformal defect. In particular, much work has been done for the correlation functions of operator insertions on the Wilson loop in the fundamental representation. In this paper, we extend such analyses to Wilson loops in the large-rank symmetric and antisymmetric representations, which correspond to probe D3 and D5 branes with AdS2× S2 and AdS2× S4 worldvolume geometries, ending at the AdS5 boundary along a one-dimensional contour. We first compute the correlation functions of protected scalar insertions from supersymmetric localization, and obtain a representation in terms of multiple integrals that are similar to the eigenvalue integrals of the random matrix, but with important differences. Using ideas from the Fermi Gas formalism and the Clustering method, we evaluate their large N limit exactly as a function of the ’t Hooft coupling. The results are given by simple integrals of polynomials that resemble the Q-functions of the Quantum Spectral Curve, with integration measures depending on the number of insertions. Next, we study the correlation functions of fluctuations on the probe D3 and D5 branes in AdS. We compute a selection of three- and four-point functions from perturbation theory on the D-branes, and show that they agree with the results of localization when restricted to supersymmetric kinematics. We also explain how the difference of the internal geometries of the D3 and D5 branes manifests itself in the localization computation.

Smeared antibranes polarise in AdS

AbstractIn the recent literature it has been questioned whether the local backreaction of antibranes in flux throats can induce a perturbative brane-flux decay. Most evidence for this can be gathered for D6 branes and Dp branes smeared over 6 − p compact directions, in line with the absence of finite temperature solutions for these cases. The solutions in the literature have flat worldvolume geometries and non-compact transversal spaces. In this paper we consider what happens when the worldvolume is AdS and the transversal space is compact. We show that in these circumstances brane polarisation smoothens out the flux singularity, which is an indication that brane-flux decay is prevented. This is consistent with the fact that the cosmological constant would be less negative after brane-flux decay. Our results extend recent results on AdS7 solutions from D6 branes to AdSp+1 solutions from Dp branes. We show that supersymmetry of the AdS solutions depend on p non-trivially.

New geometries for black hole horizons

AbstractWe construct several classes of worldvolume effective actions for black holes by integrating out spatial sections of the worldvolume geometry of asymptotically flat black branes. This provides a generalisation of the blackfold approach for higher-dimensional black holes and yields a map between different effective theories, which we exploit by obtaining new hydrodynamic and elastic transport coefficients via simple integrations. Using Euclidean minimal surfaces in order to decouple the fluid dynamics on different sections of the worldvolume, we obtain local effective theories for ultraspinning Myers-Perry branes and helicoidal black branes, described in terms of a stress-energy tensor, particle currents and non-trivial boost vectors. We then study in detail and present novel compact and non-compact geometries for black hole horizons in higher-dimensional asymptotically flat space-time. These include doubly-spinning black rings, black helicoids and helicoidal p-branes as well as helicoidal black rings and helicoidal black tori in D ≥ 6.

Emergence of longitudinal 7-branes and fuzzyS4in compactification scenarios of M(atrix) theory

In M(atrix) theory, there exist membranes and longitudinal 5-branes (L5-branes) as extended objects. Transverse components of these brane solutions are known to be described by fuzzy CP^k (k=1,2), where k=1 and k=2 correspond to spherical membranes and L5-branes of CP^2 \times S^1 world-volume geometry, respectively. In addition to these solutions, we here show the existence of L7-branes of CP^3 \times S^1 geometry, introducing extra potentials to the M(atrix) theory Lagrangian. As in the cases of k=1,2, the L7-branes (corresponding to k=3) also break the supersymmetries of M(atrix) theory. The extra potentials are introduced such that the energy of a static L7-brane solution becomes finite in the large N limit where N represents the matrix dimension of fuzzy CP^3. As a consequence, fluctuations from the L7-branes are suppressed, which effectively describes compactification of M(atrix) theory down to 7 dimensions. We show that one of the extra potentials can be considered as a matrix-valued 7-form. The presence of the 7-form in turn supports a possibility of Freund-Rubin type compactification. This suggests that our modification of M(atrix) theory can also lead to a physically interesting matrix model in four dimensions. In hope of such a possibility, we further consider compactification of M(atrix) theory down to fuzzy S^4 which can be defined in terms of fuzzy CP^3. Along the way, we also find a new L5-brane solution to M(atrix) theory which has purely spherical geometry in the transverse directions.

Hidden Supersymmetry of Domain Walls and Cosmologies

We show that all domain-wall solutions of gravity coupled to scalar fields for which the world-volume geometry is Minkowski or anti-de Sitter admit Killing spinors, and satisfy corresponding first-order equations involving a superpotential determined by the solution. By analytic continuation, all flat or closed Friedmann-Lemaître-Robertson-Walker cosmologies are shown to satisfy similar first-order equations arising from the existence of "pseudo Killing" spinors.

Dirac actions for D-branes on backgrounds with fluxes

The understanding of the fermionic sector of the world-volume D-brane dynamics on a general background with fluxes is crucial in several branches of string theory like, for example, the study of nonperturbative effects or the construction of realistic models living on D-branes. In this paper, we derive a new simple Dirac-like form for the bilinear fermionic action for any Dp-brane in any supergravity background, which generalizes the usual Dirac action valid in the absence of fluxes. A non-zero world-volume field strength deforms the usual Dirac operator in the action to a generalized non-canonical one. We show how the canonical form can be re-established by a redefinition of the world-volume geometry.

D-branes in 2d Lorentzian black hole

We study D-branes in the Lorentzian signature 2D black hole string theory. We use the technique of gauged WZW models to construct the associated boundary conformal field theories. The main focus of this work is to discuss the (semi-classical) world-volume geometries of the D-branes. We also discuss comparison of our work with results in related gauged WZW models.

CURVED MEMBRANE SOLUTIONS IN D = 11 SUPERGRAVITY

We present a class of static membrane solutions, with nonflat world volume geometry, in the eleven-dimensional supergravity with source terms. This class of solutions contains supersymmetric as well as a large class of nonsupersymmetric configurations. We comment about the near horizon limit and stability of these solutions and point out an interesting relation with a certain two-dimensional dilaton gravity system.

The Atick–Witten free energy, closed tachyon condensation and deformed Poincaré symmetry

The dependence of the free energy of string theory on the temperature at T⪢ T Hag was found long ago by Atick and Witten and is F( T)∼ ΛT 2, where Λ diverges because of a tachyonic instability. We show that this result can be understood assuming that, above the Hagedorn transition, Poincaré symmetry is deformed into a quantum algebra. Physically this quantum algebra describes a non-commutative spatial geometry and a discrete Euclidean time. We then show that in string theory this deformed Poincaré symmetry indeed emerges above the Hagedorn temperature from the condensation of vortices on the world-sheet. This result indicates that the endpoint of the condensation of closed string tachyons with non-zero winding is an infinite stack of space-like branes with a given non-commutative world-volume geometry. On a more technical side, we also point out that T-duality along a circle with antiperiodic boundary conditions for space–time fermions is broken by world-sheet vortices, and the would-be T-dual variable becomes non-compact.

Tubular branes in fluxbranes

We describe the construction of new configurations of self-gravitating p-branes with worldvolume geometries of the form R 1,p−s×S s , with 1⩽ s⩽ p, i.e., tubular branes. Since such branes are typically unstable against collapse of the sphere, they must be held in equilibrium by a fluxbrane. We present solutions for string loops with non-singular horizons, as well as M5-branes intersecting over such loops. We also construct tubular branes which carry in their worldvolume a dissolved, lower-dimensional brane (as in the dielectric effect), or an F-string. However, the connection between these solutions and related configurations that have been studied earlier in the absence of brane self-gravity, is unclear. It is argued that, at least in some instances, the self-gravitating solutions do not appear to be able to reproduce stable configurations of tubular branes.

ADM worldvolume geometry

We describe the dynamics of a relativistic extended object in terms of the geometry of a configuration of constant time. This involves an adaptation of the ADM formulation of canonical general relativity. We apply the formalism to the hamiltonian formulation of a Dirac-Nambu-Goto [DNG] relativistic extended object in an arbitrary background spacetime.

Curved branes from string dualities

We describe a simple method for generating new string solutions for which the brane worldvolume is a curved space. As a starting point we use solutions with NS-NS charges combined with two-dimensional CFTs representing different parts of spacetime. We illustrate our method with many examples, some of which are associated with conformally invariant sigma models. Using U-duality, we also obtain supergravity solutions with RR charges which can be interpreted as D-branes with non-trivial worldvolume geometry. In particular, we discuss the case of a D5-brane wrapped on AdS3 × S 3, a solution interpolating between AdS3 × S 3 × 5 and AdS3 × S 3 × S 3 × , and a D3-brane wrapped over S 3 × or AdS2 × S 2. Another class of solutions we discuss involves NS5-branes intersecting over a 3-space and NS5-branes intersecting over a line. These solutions are similar to D7-brane or cosmic string backgrounds.

Noether Currents for Bosonic Branes

We consider a relativistic brane propagating in Minkowski spacetime described by any action which is local in its worldvolume geometry. We examine the conservation laws associated with the Poincaré symmetry of the background from a worldvolume geometrical point of the view. These laws are exploited to explore the structure of the equations of motion. General expressions are provided for both the linear and angular momentum for any action depending on the worldvolume extrinsic curvature. The conservation laws are examined in perturbation theory. It is shown how non-trivial solutions with vanishing energy-momentum can be constructed in higher order theories. Finally, subtleties associated with boundary terms are examined in the context of the brane Einstein–Hilbert action.

Non-commutative worldvolume geometries: D-branes on SU(2) and fuzzy spheres

The geometry of D-branes can be probed by open string scattering. If the background carries a non-vanishing B-field, the world-volume becomes non-commutative. Here we explore the quantization of world-volume geometries in a curved background with non-zero Neveu-Schwarz 3-form field strength H = dB. Using exact and generally applicable methods from boundary conformal field theory, we study the example of open strings in the SU(2) Wess-Zumino-Witten model, and establish a relation with fuzzy spheres or certain (non-associative) deformations thereof. These findings could be of direct relevance for D-branes in the presence of Neveu-Schwarz 5-branes; more importantly, they provide insight into a completely new class of world-volume geometries.

D-branes and deformation quantization

In this note we explain how world-volume geometries of D-branes can be reconstructed within the microscopic framework where D-branes are described through boundary conformal field theory. We extract the (non-commutative) world-volume algebras from the operator product expansions of open string vertex operators. For branes in a flat background with constant non-vanishing B-field, the operator products are computed perturbatively to all orders in the field strength. The resulting series coincides with Kontsevich's presentation of the Moyal product. After extending these considerations to fermionic fields we conclude with some remarks on the generalization of our approach to curved backgrounds.

On brane solutions in M (atrix) theory

In this paper we consider brane solutions of the form G/ H in M(atrix) theory, showing the emergence of world volume coordinates for the cases where G = SU( n). We examine a particular solution with a world volume geometry of the form C P 2 × S1 in some detail and show how a smooth manifold structure emerges in the large N limit. In this limit the solution becomes static; it is not supersymmetric but is part of a supersymmetric set of configurations. Supersymmetry in small locally flat regions can be obtained, but this is not globally defined. A general group theoretic analysis of the previously known spherical brane solutions is also given.