We study Berry's phase in the D0-D4-brane system. When a D0-brane moves in the background of D4-branes, the first excited states undergo a holonomy described by a non-Abelian Berry connection. At weak coupling this is an SU(2) connection over R^5, known as the Yang monopole. At strong coupling, the holonomy is recast as the classical gravitational precession of a spinning particle. The Berry connection is the spin connection of the near-horizon limit of the D4-branes, which is a continuous deformation of the Yang and anti-Yang monopole.
We analyze thoroughly the boundary conditions allowed in classical non-linear sigma models and derive from first principle the corresponding geometric objects, i.e. D-branes. In addition to giving classical D-branes an intrinsic and geometric foundation, D-branes in nontrivial H flux and D-branes embedded within D-branes are precisely defined. A well known topological condition on D-branes is replaced.
The perihelion precession, the deflection of light, and the radar echo delay are classical tests of General Relativity here used to probe brane world topologically charged black holes in a f(R) bulk and to constrain the parameter that arises from the Shiromizu-Maeda-Sasaki procedure applied to a f(R) bulk as well. The existing Solar system observational data constrain the possible values of the tidal charge parameter and the effective cosmological constant including f(R) brane world effects. We show that the observational/experimental data for both perihelion precession and radar echo delay ma…
The algebraic definition of charges for symmetry-preserving D-branes in Wess-Zumino-Witten models is shown to coincide with the geometric definition, for all simple Lie groups. The charge group for such branes is computed from the ambiguities inherent in the geometric definition.
We investigate models in which inflation is driven by a single geometrical tachyon. We assume that the D-brane as a probe brane in the background of NS5-branes has non-zero angular momentum which is shown to play similar role as the number of the scalar fields of the assisted inflation. We demonstrate that the angular momentum corrected effective potential allows to account for the observational constraint on COBE normalization, spectral index $n_S$ and the tensor to scalar ratio of perturbations consistent with WMAP seven years data.
Recently it has been suggested to use the perigee of the proposed LARES/WEBER-SAT satellite in order to measure the secular precession which would be induced on such Keplerian orbital element by a weak-field modification of gravity occurring in some Brane-World scenarios put forth by Dvali, Gabadadze and Porrati. This precession, derived for the first time by Lue and Starkman, amounts to 4\times 10-3 milliarcseconds per year for an Earth orbiting satellite. In this paper we show that, according to the recently released EIGEN-CG01C Earth gravity model the quite larger systematic errors due to t…
New forms of Born-Infeld, D-brane and M theory five-brane actions are found which are quadratic in the abelian field strength. The gauge fields couple both to a background or induced metric and a new auxiliary metric, whose elimination reproduces the non-polynomial Born-Infeld action. This is similar to the introduction of an auxiliary metric to simplify the Nambu-Goto string action. This simplifies the quantisation and dualisation of the gauge fields.
We explore the differential geometry of T-duality and D-branes. Because D-branes and RR-fields are properly described via K-theory, we discuss the (differential) K-theoretic generalization of T-duality and its application to the coupling of D-branes to RR-fields. This leads to a puzzle involving the transformation of the A-roof genera in the coupling.
We study world-volume effective theories of five-branes in type II string theories. We determine the bosonic zero-modes of the NS5-brane, the Kaluza-Klein monopole, the exotic Q5-, R5-branes and a space-filling brane, by direct calculations within the formalism of double field theory (DFT). We show that these zero-modes are Nambu-Goldstone modes associated with the spontaneously broken gauge symmetries in DFT. They are organized into the bosonic part of the six-dimensional $\mathcal{N} = (1,1)$ vector and the $\mathcal{N} = (2,0)$ tensor multiplets. Among other things, we examine the locally n…
By blowing up the ambient space along the curve wrapped by B-branes, we study the brane superpotentials and Ooguri-Vafa invariants on complete intersections Calabi-Yau threefolds. On the topological B-model side, B-brane superpotentials are expressed in terms of the period integral of the blow-up manifolds. By mirror maps, the superpotentials are generating functions of Ooguri-Vafa invariants counting holomorphic disks on the topological A-model side.
We present an explicit relation between the Hanany-Witten and Geometric Engineering approaches of realising gauge theories in string theory. The last piece in the puzzle is a T-duality relating arbitrary Hanany-Witten setups and fractional branes.
When string/M-theory is compactified to lower dimensions, the U-duality symmetry predicts so-called exotic branes whose higher dimensional origin cannot be explained by the standard string/M-theory branes. We argue that exotic branes can be understood in higher dimensions as non-geometric backgrounds or U-folds, and that they are important for the physics of systems which originally contain no exotic charges, since the supertube effect generically produces such exotic charges. We discuss the implications of exotic backgrounds for black hole microstate (non-)geometries.
In arXiv:0801.0218 [hep-th] it was conjectured that quantum effects of open strings moving on D-branes generate the D-brane geometry through a counter-vertex operator. The conjecture has been checked at one-loop in arXiv:0806.3330 [hep-th]. Here we discuss the two-loop extension.
We study how non-perturbative dynamics on D-branes affects the ten-dimensional geometry. We show that a gaugino condensate changes the complex and the symplectic structures of the original manifold by deforming the supersymmetry conditions. The cases of D5, D6 and D7-branes are discussed in detail. In the latter case we find the explicit form of the resulting back-reacted background at linear order in the gaugino condensate.
The double field theory monopole solution by Berman and Rudolph is shown to reproduce non-geometric backgrounds with non-vanishing Q- and R-flux upon an appropriate choice of physical and dual coordinates. The obtained backgrounds depend non-trivially on dual coordinates and have only trivial monodromies. Upon smearing the solutions along the dual coordinates one reproduces the known $5^2_2$ solution for the Q-brane and co-dimension 1 solution for the R-brane. The T-duality invariant magnetic charge is explicitly calculated for all these backgrounds and is found to be equal to the magnetic cha…
The compactness of the closed string in the classical Type II string theory reveals the duality, whereas the compactness of the open string reveals that the end of the string is on the hypersurface which satisfies the Dirichlet boundary condition.
In this short printed version of my talk I consider the generalized action for super-p-branes proposed previously in collaboration with D. Sorokin and Dmitrij V. Volkov. I describe briefly, the derivation doubly supersymmetric geometric approach from the generalized action and discuss one of the direction of its possible application.
We study T-duality chains of five-branes in heterotic supergravity where the first order $α'$-corrections are present. By performing the $α'$-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and the exotic $5^2_2$-brane solutions associated with the symmetric, the neutral and the gauge NS5-branes. We find that the Yang-Mills gauge field in these solutions satisfies the self-duality condition in the three- and two-dimensional transverse spaces to the brane world-volumes. The $O(2,2)$ monodromy structures of the $5^2_2$-brane solutions are investi…
We use the permutation symmetry between the product of several group manifolds in combination with orbifolds and T-duality to construct new classes of symmetry breaking branes on products of group manifolds. The resulting branes mix the submanifolds and break part of the diagonal chiral algebra of the theory. We perform a Langrangian analysis as well as a boundary CFT construction of these branes and find agreement between the two methods.
In a recent paper (hep-th/0703157), Sen studied unstable D-branes in NS5-branes backgrounds and argued that in the strong curvature regime the universal open string tachyon (on D-branes of the wrong dimensionality) and the geometric tachyon (on D-branes that are BPS in flat space but not in this background) may become equivalent. We study in this note an example of a non-BPS suspended D-brane vs. a BPS D-brane at equal distance between two fivebranes. We use boundary worldsheet CFT methods to show that these two unstable branes are identical.
This is a brief review of some recent results on the geometric approach to symmetric D-branes in group manifolds, both twisted and untwisted. We describe the geometry of the gluing conditions and the quantisation condition in the boundary WZW model, and we illustrate this by determining the consistent twisted and untwisted D-branes in the Lie group SU_3.
From the worldsheet perspective, the superpotential on a D-brane wrapping internal cycles of a Calabi-Yau manifold is given as a generating functional for disk correlation functions. On the other hand, from the geometric point of view, D-brane superpotentials are captured by certain chain integrals. In this work, we explicitly show for branes wrapping internal 2-cycles how these two different approaches are related. More specifically, from the worldsheet point of view, D-branes at the Landau-Ginzburg point have a convenient description in terms of matrix factorizations. We use a formula derive…
In this paper we discuss the construction of non-geometric Q- and R-branes as sources of non-geometric Q- and R-fluxes in string compactifications. The non-geometric Q-branes, being obtained via T-duality from the NS 5-brane or respectively from the KK-monopole, are still local solutions of the standard NS action, where however the background fields G and B possess non-geometric global monodromy properties. We show that using double field theory, redefined background fields tilde G and beta as well as their corresponding effective action, the Q-branes are locally and globally well behaved solu…
Geometrically non-Higgsable seven-branes carry gauge sectors that cannot be broken by complex structure deformation, and there is growing evidence that such configurations are typical in F-theory. We study strongly coupled physics associated with these branes. Axiodilaton profiles are computed using Ramanujan's theories of elliptic functions to alternative bases, showing explicitly that the string coupling is order one in the vicinity of the brane; that it sources nilpotent $SL(2,\mathbb{Z})$ monodromy and therefore the associated brane charges are modular; and that essentially all F-theory co…
For D-brane system with three D-branes on compact Calabi-Yau threefolds, the dual F-theory fourfolds for parallel/complete coincident/part coincident D-brane system is constructed by the type II/F-theory duality. Complete coincident means that the three D-branes coincide and part coincident represents the coincident of two of the three D branes. The low energy effective superpotentials are calculated by mirror symmetry, GKZ-system method and the type II/F-theory duality on the B-model side, respectively. Using the mirror symmetry, A-model superpotentials and the Ooguri-Vafa invariants are obta…
The geometric description of D-branes in WZW models is pushed forward. Our starting point is a gluing condition\, $J_{+}=FJ_-$ that matches the model's chiral currents at the worldsheet boundary through a linear map $F$ acting on the WZW Lie algebra. The equivalence of boundary and gluing conditions of this type is studied in detail. The analysis involves a thorough discussion of Frobenius integrability, shows that $F$ must be an isometry, and applies to both metrically degenerate and nondegenerate D-branes. The isometry $F$ need not be a Lie algebra automorphism nor constantly defined over th…
We extend the $P$-flux analysis carried out recently on the $T^6/[\mathbb{Z}_2 \times \mathbb{Z}_2 ]$ type-II orientifold model to include all the possible non-geometric fluxes. By deriving universal T-duality rules for all the fluxes, we are able to write down a complete expression for the superpotential for both the IIB and IIA theories. By exploiting the universal T-duality rules that apply to all the branes in string theory, we then identify all the exotic branes that can be consistently included to cancel the tadpoles induced by the fluxes. Finally, we derive the representations of these …
A system of k Neveu-Schwarz (NS) 5-branes of type II string theory with one transverse direction compactified on a circle admits various unstable D-brane systems, - some with geometric instability arising out of being placed at a point of unstable equilibrium in space and some with the usual open string tachyonic instability but no geometric instability. We discuss the effect of NS 5-branes on the descent relations among these branes and their physical interpretation in the T-dual ALF spaces. We argue that if the tachyon potential controlling these descent relations obeys certain conditions, t…
We study the assisted inflation scenario from the rolling of $N$ BPS D3-brane into the NS5-branes, on a transverse geometry of $R^3 \times S^1$, coupled to four dimensional gravity. We assume that the branes are distributed along $S^1$ and the probe D3-branes spin along $R^3$ plane. Qualitatively this process is similar to that of N-tachyon assisted inflation on unstable D-branes. We further study the spinflation scenario numerically and analyze its effect.
We present a detailed analysis of our recent observation that the origin of the geometric tachyon, which arises when a D$p$-brane propagates in the vicinity of a stack of coincident NS5-branes, is due to the proper acceleration generated by the background dilaton field. We show that when a fundamental string (F-string), described by the Nambu-Goto action, is moving in the background of a stack of coincident D$p$-branes, the geometric tachyon mode can also appear since the overall conformal mode of the induced metric for the string can act as a source for proper acceleration. We also studied th…
We consider geometric engineering of N=1 supersymmetric QFTs with matter in terms of a local model for compactification of F-theory on Calabi-Yau fourfold. By bringing 3-branes near 7-branes we engineer N=1 supersymmetric $SU(N_c)$ gauge theory with $N_f$ flavors in the fundamental. We identify the Higgs branch of this system with the instanton moduli space on the compact four dimensional space of the 7-brane worldvolume. Moreover we show that the Euclidean 3-branes wrapped around the compact part of the 7-brane worldvolume can generate superpotential for $N_f=N_c-1$ as well as lead to quantum…
We investigate boundary dynamics of orbifold conformal field theory involving T-duality twists. Such models typically appear in contexts of non-geometric string compactifications that are called monodrofolds or T-folds in recent literature. We use the framework of boundary conformal field theory to analyse the models from a microscopic world-sheet perspective. In these backgrounds there are two kinds of D-branes that are analogous to bulk and fractional branes in standard orbifold models. The bulk D-branes in T-folds allow intuitive geometrical interpretations and are consistent with the class…
Orientifold vacua allow the simultaneous presence of supersymmetric bulks, with one or more gravitinos, and non-supersymmetric combinations of BPS branes. This ``brane supersymmetry breaking'' raises the issue of consistency for the resulting gravitino couplings, and Dudas and Mourad recently provided convincing arguments to this effect for the ten-dimensional $USp(32)$ model. These rely on a non-linear realization of local supersymmetry {\it à la} Volkov-Akulov, although no gravitino mass term is present, and the couplings have a nice geometrical interpretation in terms of ``dressed'' bulk fi…
In the literatures, several types of thick smooth brane configurations in a pure geometric Weyl integrable 5-dimensional space time have been presented. The Weyl geometry is a non-Riemannian modification of 5-dimensional Kaluza--Klein (KK) theory. All these thick brane solutions preserve 4-dimensional Poincaré invariance, and some of them break $Z_2$--symmetry along the extra dimension. In this paper, we study localization of various matter fields on these pure geometrical thick branes, which also localize the graviton. We present the shape of the potential of the corresponding Schr$\mathrm{\d…
We discuss aspects of topological B-type D-branes in the framework of the derived category of coherent sheaves on a Calabi-Yau 3-fold X. We analyze the link between massless D-branes and monodromies in the CFT moduli space. A classification of all massless D-branes at any point in the moduli space is conjectured, together with an associated monodromy. We test the conjectures in two independent ways. First we establish a composition formula for certain Fourier-Mukai functors, which is a consequence of the triangulated structure of D(X). Secondly, using pi-stability we rederive the stable solito…
We use large N duality to study brane/anti-brane configurations on a class of Calabi-Yau manifolds. With only branes present, the Calabi-Yau manifolds in question give rise to N=2 ADE quiver theories deformed by superpotential terms. We show that the large N duality conjecture of hep-th/0610249 reproduces correctly the known qualitative features of the brane/anti-brane physics. In the supersymmetric case, the gauge theories have Seiberg dualities which are represented as flops in the geometry. Moreover, the holographic dual geometry encodes the whole RG flow of the gauge theory. In the non-sup…
In string theory D-branes can be classified by the RR-charge they carry. In the simplest case the quantized RR-charge takes values in K-theory of the spacetime manifold. However, if the D-brane worldvolume is not spin^c or if there is a background B-field present, the Freed-Witten anomaly cancellation condition requires the RR-charge to take values in twisted K-theory. Twisted K-theory can be defined using the language of noncommutative geometry, thus opening up a possibility for noncommutative generalizations, in particular of the Minasian-Moore formula for the classical approximation of the …
We consider the field theories on multiple stacks of D5 branes wrapped on four cycles of resolved/deformed conifold geometries fibered over a two torus. The central charges of the D5 branes are slightly misaligned when the branes are wrapped on various rigid holomorphic two cycles or when they have different charges with respect to a magnetic flux turned on the two torus. The wrapped D5 branes preserve (0,2) supersymmetry in two dimensions if the Kahler moduli and the magnetic flux are related. Our geometries are T-dual to the brane configurations considered by Kutasov-Lin and we provide a geo…
In this work we study the generalization of twisted homology to geometric and non-geometric backgrounds. In the process we describe the necessary conditions to wrap a network of D-branes on twisted cycles. If the cycle is localized in time, we show how by an instantonic brane mediation, some D-branes transform into fluxes on different backgrounds including non-geometric fluxes. As a consequence, we show that in the case of a IIB six-dimensional torus compactification on a simple orientifold, the flux superpotential is not invariant by this brane-flux transition, allowing the connection among d…
We study Vafa's geometric transition from a brane setup in M-theory. In this transition D5 branes wrapped on P^1 cycles of a resolved conifold disappear and are replaced by fluxes on a deformed conifold. In the limit of small sized P^1, we describe this mechanism as a transition from curved M5 branes to plane M5 branes which replaces SU(N) MQCD by U(1) theories on the bulk. This agrees with the results expected from the geometric transition. We also discuss the reduction to ten dimensions and a brane creation mechanism in the presence of fluxes.
We study the effect of rolling of N D3-branes in the vicinity of NS5-branes. We find out that this system coupled with the four dimensional gravity gives the slow roll assisted inflation of the scalar field theory. Once again this expectation is exactly similar to that of N-tachyon assisted inflation on unstable D-branes.
Unstable, non-BPS D-branes in weakly coupled ten dimensional string theory have many mysterious properties. Among other things, it is not clear what sets their tension, what is their relation to the better understood BPS D-branes, and why the open string tachyon on them is described by an effective Lagrangian which suggests that the tachyon corresponds to an extra spatial dimension transverse to the branes. We point out that the dynamics of D-branes in the presence of Neveu-Schwarz fivebranes on a transverse R^3 times S^1 provides a useful toy model for studying these issues. From the point of…
Geometrical coupling in a co-dimensional one Randall-Sundrum scenario (RS) is used to study resonances of $p-$form fields. The resonances are calculated using the transfer matrix method. The model studied consider the standard RS with delta-like branes, and branes generated by kinks and domain-wall as well. The parameters are changed to control the thickness of the smooth brane. With this a very interesting pattern is found for the resonances. The geometrical coupling does not generate resonances for the reduced $p-$form in all cases considered.
We investigate the low-energy effective description of non-geometric compactifications constructed by T-dualizing two or three of the directions of a T^3 with non-vanishing H-flux. Our approach is to introduce a D3-brane in these geometries and to take an appropriate decoupling limit. In the case of two T-dualities, we find at low energies a non-commutative T^2 fibered non-trivially over an S^1. In the UV this theory is still decoupled from gravity, but is dual to a little string theory with flavor. For the case of three T-dualities, we do not find a sensible decoupling limit, casting doubt on…
We consider Kaluza Klein reductions of M-theory on the Z_N orbifold of the spin bundle over S^3 along two different U(1) isometries. The first one gives rise to the familiar ``large N duality'' of the N=1 SU(N) gauge theory in which the UV is realized as the world-volume theory of N D6-branes wrapped on S^3, whereas the IR involves N units of RR flux through an S^2. The second reduction gives an equivalent version of this duality in which the UV is realized geometrically in terms of an S^2 of A_{N-1} singularities, with one unit of RR flux through the S^2. The IR is reached via a geometric tra…
We construct several geometric representatives for the C^n/Z_m fractional branes on either a partially or the completely resolved orbifold. In the process we use large radius and conifold-type monodromies, and provide a strong consistency check. In particular, for C^3/Z_5 we give three different sets of geometric representatives. We also find the explicit Seiberg-duality, in the Berenstein-Douglas sense, which connects our fractional branes to the ones given by the McKay correspondence.
We study D-branes on abelian orbifolds C^d/Z_N for d=2, 3. The toric data describing the D-brane vacuum moduli space, which represents the geometry probed by D-branes, has certain redundancy compared with the classical geometric description of the orbifolds. We show that the redundancy has a simple combinatorial structure and find analytic expressions for degrees of the redundancy. For d=2 the structure of the redundancy has a connection with representations of SU(N) Lie algebra, which provides a new correspondence between geometry and representation theory. We also prove that non-geometric ph…
We apply noncommutative geometry to a system of N parallel D-branes, which is interpreted as a quantum space. The Dirac operator defining the quantum differential calculus is identified to be the supercharge for strings connecting D-branes. As a result of the calculus, Connes' Yang-Mills action functional on the quantum space reproduces the dimensionally reduced U(N) super Yang-Mills action as the low energy effective action for D-brane dynamics. Several features that may look ad hoc in a noncommutative geometric construction are shown to have very natural physical or geometric origin in the D…
The motion of a Dp-brane in the background of a stack of coincident NS5-branes is analysed as the motion of a relativistic point particle in the transverse space of the five-branes. In this system, the particle experiences a proper acceleration orthogonal to its proper velocity due to the background dilaton field which changes the dynamics from that of a simple geodesic motion. In particular, we show that in the vicinity of the five-branes, it is this acceleration which is responsible for modifying the motion of the radial mode to that of an inverted simple harmonic oscillator leading to the t…
We consider the interplay between brane constructions and type IIA, IIB or M-theory geometries on Calabi-Yau (CY) and G_2 holonomy manifolds. This is related to N=1 (and N=2) gauge theories in four dimensions. We first discuss simple geometric transitions corresponding to brane set ups involving orthogonal (or parallel) Neveu-Schwarz branes that approach each other. This is related to confinement and Seiberg duality in SQCD. In particular, we argue that in type IIA, a CP^1 of singularities and one unit of Ramond-Ramond (RR) flux is dual to a D6 brane wrapped on a Lens space, describing the UV …
Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2's. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2's causes discrete jumps in the energeti…
We study four-dimensional N=1 gauge theories arising on D3-branes probing toric singularities. Toric dualities and flows between theories corresponding to different singularities are analyzed by encoding the geometric information into (p,q) webs. A new method for identifying global symmetries of the four-dimensional theories using the brane webs is developed. Five-dimensional theories are associated to the theories on the D3-branes by using (p,q) webs. This leads to a novel interpretation of Seiberg duality, as crossing curves of marginal stability in five dimensions.
In this paper we consider a geometrical Yukawa coupling as a solution to the problem of gauge field localization. We show that upon dimensional reduction the vector field component of the field is localized but the scalar component ($A_5$) is not. We show this for any smooth version of the Randall-Sundrum model. The covariant version of the model with geometrical coupling simplify the generalization to smooth versions generated by topological defects. This kind of model has been considered some time ago, but there it has been introduced two free parameters in order to get a localized solution …
In this note we study T-duality transformations for the NS5-brane and its orbifolds along angular directions. We identify a geometric charge for these configurations and show that it is interchanged with the H-flux under T-duality. We furthermore perform a supersymmetry analysis and find that T-duality can break supersymmetry, in agreement with earlier results in the literature. We contrast our findings to compactifications of the NS5-brane on tori, which have vanishing geometric charge and for which T-duality transformations along the compact directions preserve supersymmetry. This shows that…
We propose a general method to study open/closed string dualities from transitions in M theory which is valid for a large class of geometrical configurations. By T-duality we can transform geometrically engineered configurations into N = 1 brane configurations and study the transitions of the corresponding branes by lifting the configurations to M-theory. We describe the transformed degenerated M5 branes and extract the field theory information on gluino condensation by factorization of the Seiberg-Witten curve. We also include massive flavors and orientifolds and discuss Seiberg duality which…
We study how exotic branes, i.e. branes whose tensions are proportional to $g_s^{-α}$, with $α>2$, are realised in Exceptional Field Theory (EFT). The generalised torsion of the Weitzenböck connection of the $\operatorname{SL}(5)$ EFT which, in the language of gauged supergravity describes the embedding tensor, is shown to classify the exotic branes whose magnetic fluxes can fit into four internal dimensions. By analysing the weight diagrams of the corresponding representations of $\operatorname{SL}(5)$ we determine the U-duality orbits relating geometric and non-geometric fluxes. As a further…
