We study non-perturbative effects in four-dimensional N=1 supersymmetric orientifold compactifications due to D-brane instantons which are generically not invariant under the orientifold projection. We show that they can yield superpotential contributions via a multi-instanton process at threshold. Some constituents of this configuration form bound states away from the wall of marginal stability which can decay in other regions of moduli space. A microscopic analysis reveals how contributions to the superpotential are possible when new BPS states compensate for their decay. We study this concretely for D2-brane instantons along decaying special Lagrangians in Type IIA and for D5-branes instantons carrying holomorphic bundles in Type I theory.
We show that the BPS configurations of uniform field strength can be interpreted as those for sheets of infinite number of BPS magnetic monopoles, and found that the number of normalizable zero modes per each magnetic monopole charge is four. We identify monopole sheets as the intersecting planes of D3 branes. Similar analysis on self-dual instanton configurations is worked out and the number of zero modes per each instanton number is found to match that of single isolated instanton.
We investigate the instanton effects of non-BPS D0-brane in type I string theory. We argue the general properties of these instanton effects and consider these on $R^9\times S^1$ as a simple example using the effective action of D0-brane.
The one-instanton contribution to a circular BPS Wilson loop in N=4 SU(2) Yang--Mills theory is evaluated in semiclassical approximation. This article amplifies part of a talk given by MBG at the Strings 2001 conference, Mumbai, India (January 5-10, 2001). The results are preliminary and a more complete exposition will be contained in a forthcoming paper.
According to the covariant open superstring description of 1/2-BPS D-branes in the AdS$_5\times$S$^5$ background, there are two kinds of purely instantonic D-branes. One is the well known D(-1)-brane or D-instanton, and another is the D1-brane spanning a two dimensional subspace inside S$^5$. We identify the actual 1/2-BPS instantonic D1-brane configurations and their supersymmetry structures. From the results, it is concluded that any spherical D1-instanton with the radius equal to that of S$^5$ is 1/2-BPS. After evaluating the 1/2-BPS D1-instanton action, we discuss the relation of D1-instan…
According to the covariant open superstring description of D-branes in the AdS$_4 \times \mathbf{CP}^3$ background, 1/2-BPS D2-branes are purely instantonic. Based on this and by taking the eleven dimensional viewpoint, we identify the 1/2-BPS instantonic M2-brane configurations in the AdS$_4 \times$ S$^7 / \mathbf{Z}_k$ background, which reduces to the AdS$_4 \times \mathbf{CP}^3$ under the large $k$ limit, and evaluate their action values. We also consider the previously known 1/2-BPS instantonic objects in ten dimensions from the M2-brane viewpoint to compare with our results.
We study instanton corrections to the vacuum expectation value (VEV) of 1/6 BPS Wilson loops in ABJM theory from the Fermi gas approach. We mainly consider Wilson loops in the fundamental representation and winding Wilson loops, but we also initiate the study of Wilson loops with two boundaries. We find that the membrane instanton corrections to the Wilson loop VEV are determined by the refined topological string in the Nekrasov-Shatashvili limit, and the pole cancellation mechanism between membrane instantons and worldsheet instantons works also in the Wilson loop VEVs as in the case of the p…
We consider non-perturbative terms in the 4d effective action due to BPS D-brane instantons, and study their continuity properties in moduli space as instantons cross lines of BPS stability, potentially becoming non-BPS. We argue that BPS instantons contributing to the superpotential cannot become non-BPS anywhere in moduli space, since they cannot account for the required four goldstino fermion zero modes. At most they can reach lines of threshold stability, where they split into mutually BPS multi-instantons, as already discussed in the literature. On the other hand, instantons with addition…
We extend the recent conjecture on the relation between a certain 1/8 BPS subsector of 4d N=4 SYM on S^2 and 2d Yang-Mills theory by turning on circular 1/2 BPS 't Hooft operators linked with S^2. We show that localization predicts that these 't Hooft operators and their correlation functions with Wilson operators on S^2 are captured by instanton contributions to the partition function of the 2d Yang-Mills theory. Based on this prediction, we compute explicitly correlation functions involving the 't Hooft operator, and observe precise agreement with S-duality predictions.
In this paper we would like to show that from N non-BPS D0-branes in type IIB theory we can obtain all BPS and non-BPS D-branes through the tachyon condensation in the large N limit.
This paper is devoted to the study of non-BPS Dp-branes in the presence of NS5-branes on transverse R^3xS^1.We will formulate the tachyon effective action in this background and then we will discuss its properties. Then we will study the solutions of the equations of motion that describe lower dimensional BPS and non-BPS D-branes.
BPS instantons are discussed in Lifshitz-type anisotropic field theories. We consider generalizations of the sigma model/Yang-Mills instantons in renormalizable higher dimensional models with the classical Lifshitz scaling invariance. In each model, BPS instanton equation takes the form of the gradient flow equations for "the superpotential" defining "the detailed balance condition". The anisotropic Weyl rescaling and the coset space dimensional reduction are used to map rotationally symmetric instantons to vortices in two-dimensional anisotropic systems on the hyperbolic plane. As examples, w…
We review the recent developments in our understanding of non-BPS states and branes in string theory. The topics include 1) construction of unstable non-BPS D-branes in type IIA and type IIB string theories, 2) construction of stable non-BPS D-branes on various orbifolds and orientifolds of type II string theories, 3) description of BPS and non-BPS D-branes as tachyonic soliton solutions on brane-antibrane pair of higher dimension, and 4) study of the spectrum of non-BPS states and branes on a system of coincident D-brane - orientifold plane system. Some other related results are also discusse…
We construct unstable system D8-brane+D8-antibrane as a kink solution on world-volume of non-BPS D9-brane in Type IIA theory. Further we will make other checks confirming validity of our appro.
This paper contains the results of our investigations of BPS instantons and of our work on N=2 supersymmetric gauge theories. The BPS instantons we study appear in type II string theory compactifications on Calabi-Yau threefolds. In the corresponding four-dimensional effective supergravity actions the BPS instantons arise as finite action solutions to the Euclidean equations of motion. For N=2 supersymmetric gauge theories we construct general Lagrangians involving gauge groups with (non-abelian) electric and magnetic (dyonic) charges. In this work a coupling to hypermultiplets is included.
We construct an effective action describing brane-antibrane system containing N D-branes and N \bar{D}-branes. BPS equations for remaining D-branes after tachyon condensation are derived and their properties are investigated. The value of the D-brane tension and the number of brane bound states are discussed.
In this paper we would like to show simple mechanisms how from the action for non-BPS D-brane we can obtain action describing BPS D(p-1)-brane in Type IIA theory.
We construct an exact soliton, which represents a BPS Dp-brane, in a boundary string field theory action of infinitely many non-BPS D(p-1)-branes. Furthermore, we show that this soliton can be regarded as an exact soliton in the full string field theory. The world-volume theory of the BPS Dp-brane constructed in this way becomes usual gauge theory on commutative R^{p+1}, instead of non-commutative plane. We also construct a D$p$-brane from non-BPS D(p-n)-branes by the ABS like configuration. We confirm that the Dp-brane has correct RR charges and the tension.
We find Carroll non-BPS Dp-brane action by performing Carroll limit of a canonical form of unstable Dp-brane action. We analyze different Carroll limits and discuss solutions of the equations of motion of Carroll non-BPS Dp-brane at the tachyon vacuum.
When instantons are put into the Higgs phase, vortices are attached to instantons. We construct such composite solitons as 1/4 BPS states in five-dimensional supersymmetric U(Nc) gauge theory with Nf(>=Nc) fundamental hypermultiplets. We solve the hypermultiplet BPS equation and show that all 1/4 BPS solutions are generated by an Nc x Nf matrix which is holomorphic in two complex variables, assuming the vector multiplet BPS equation does not give additional moduli. We determine the total moduli space formed by topological sectors patched together and work out the multi-instanton solution insid…
In this paper we will consider the dynamics of BPS and non-BPS Dp-branes in the background of N Dk-branes. Our approach is based on an existence of the new symmetry of D-brane effective actions that naturally emerges in the near horizon region of the stack of N Dk-branes. Since generally this scaling symmetry is explicitly broken in the Lagrangian we will find the equation that determines the time evolution of the generator of this transformations. Then we will argue that in case when the tachyon living on the worldvolume of unstable D-brane reaches the stable minimum the time evolution of thi…
We construct 1/8, 1/4, and 1/2 BPS solutions spanned by diagonal elements of U(N) constant fluxes in the 6+1 dimensional U(N) super Yang-Mills theory on T^6 with topological stability. These solutions represent BPS bound states of D0, D2, D4, and D6 branes. The consistency with the D-brane charge conservation implies that unstable D0-D2-D6-brane systems in a B field decay to the BPS solutions, in which lower dimensional D-branes are dissolved in D6-branes.
The BPS method is used to find BPS solutions of the worldvolume theory of a D5-brane in the near horizon geometry of a D3-brane. The BPS bound is interpreted in terms of the `maximally extended' D5 worldvolume supersymmetry algebra in the corresponding curved background, which is OSp(1|16). This algebra is an extension of the worldvolume superalgebra OSp(4^*|4). The analysis is generalized to the non-near horizon case.
We use tachyon field theory effective action to study the dynamics of a non-BPS Dp-brane propagating in the vicinity of k NS5-branes. For the time dependent tachyon condensation we will concentrate on the case of the large tachyon and the case when a non-BPS D-brane is close to NS5-branes. For spatial dependent tachyon condensation we will argue that the problem reduces to the study of the motion of an array of D(p-1)-branes and D(p-1)-antibranes in the vicinity of k NS5-branes.
The standard prescription for computing Wilson loops in the AdS/CFT correspondence in the large coupling regime and tree-level involves minimizing the string action. In many cases the action has more than one saddle point as in the simple example studied in this paper, where there are two 1/4 BPS string solutions, one a minimum and the other not. Like in the case of the regular circular loop the perturbative expansion seems to be captured by a free matrix model. This gives enough analytic control to extrapolate from weak to strong coupling and find both saddle points in the asymptotic expansio…
We study how non-BPS type II D-branes couple to R-R potentials. Upon tachyon condensation the couplings we find give rise to the Wess-Zumino action of BPS D-branes.
We investigate D-branes in a Z_3xZ_3 orbifold with discrete torsion. For this class of orbifolds the only known objects which couple to twisted RR potentials have been non-BPS branes. By using more general gluing conditions we construct here a D-brane which is BPS and couples to RR potentials in the twisted and in the untwisted sectors.
We construct non-relativistic non-BPS Dp-brane action. Then we will study the properties of the tachyon kink solution on its world-volume. We will argue that this tachyon kink describes non-relativistic D(p-1)-brane.
We consider the behaviour of neutral non-BPS branes probed by scalars and gravitons. We show that the naked singularity of the non-BPS branes is a {\it repulson} absorbing no incoming radiation. The naked singularity is surrounded by an infinite potential well breaking the unitarity of the scattering S-matrix. We compute the absorption cross section which is infrared divergent. In particular this confirms that gravity does not decouple for the non-BPS branes.
In this short note we would like to propose a form for the action of a non-BPS D-brane, which will be manifestly supersymmetric invariant and T-duality covariant. We also explicitly show that tachyon condensation on the world-volume of this brane leads to the Dirac-Born-Infeld action for BPS D(p-1)-brane.
Non-BPS dyon solutions to D3-brane actions are constructed when one or more scalar fields describing transverse fluctuations of the brane, are considered. The picture emerging from such non-BPS configurations is analysed, in particular the response of the D-brane-string system to small perturbations.
We perform Hamiltonian analysis of non-relativistic non-BPS Dp-brane. We find the constraint structure of this theory and determine corresponding equations of motion. We further discuss property of this theory at the tachyon vacuum.
We reconsider dyonic p-brane solutions derivable from Liouville and Toda integrable systems and investigate their geometric structure. It is shown that the non-BPS non-black dyonic branes are not regular on the horizon.
We investigate the effective action for a non-BPS brane in a time-depending embedding. This action is considered as the action for tachyon and embedding coupled to the brane gravity. We derive the slow roll parameters from this model.
We extensively study BPS solutions of the low energy effective theory of M5-brane in large C-field background. This provides us an opportunity to explore the interactions turned on by C-field background through the Nambu-Poisson structure. The BPS states considered in this paper include the M-waves, the self-dual string (M2 ending on M5), tilted M5-brane, holomorphic embedding of M5-brane and the intersection of two M5-branes along a 3-brane.
Systems of D3-branes at orientifold singularities can receive non-perturbative D-brane instanton corrections, inducing field theory operators in the 4d effective theory. In certain non-chiral examples, these systems have been realized as the infrared endpoint of a Seiberg duality cascade, in which the D-brane instanton effects arise from strong gauge theory dynamics. We present the first UV duality cascade completion of chiral D3-brane theories, in which the D-brane instantons arise from gauge theory dynamics. Chiral examples are interesting because the instanton fermion zero mode sector is to…
A new class of six-dimensional asymmetric orientifolds is considered where the orientifold operation is combined with T-duality. The models are supersymmetric in the bulk, but the cancellation of the tadpoles requires the introduction of brane configurations that break supersymmetry. These can be described by D7-brane anti-brane pairs, non-BPS D8-branes or D9-brane anti-brane pairs. The transition between these different configurations and their stability is analysed in detail.
We present a candidate supergravity solution for a stacked configuration of stable non-BPS D-branes in Type II string theory compactified on T^4/Z_2. This gives a supergravity description of nonabelian tachyon condensation on the brane worldvolume.
We apply ideas that have appeared in the study of D-branes on Calabi-Yau compactifications to the derivation of the BPS spectrum of field theories. In particular, we identify an orbifold point whose fractional branes can be thought of as ``partons'' of the BPS spectrum of N=2 pure SU(N) SYM. We derive the BPS spectrum and lines of marginal stability branes near that orbifold, and compare our results with the spectrum of the field theories.
We derive the BPS mass formulae of the Dirichlet branes from the Born-Infeld type action. BPS saturation is realized when the brane has the minimal volume while keeping the appropriate winding numbers. We apply the idea to two cases, type IIA superstring compactified on $T^4$ and $K3$. The result is consistent with the string duality, and the expected spectrum for the BPS states is reproduced.
The non-abelian flat directions in the tachyon potential of stable non-BPS branes recently found are shown to persist to all orders in alpha' at tree level in the string coupling. We also obtain the non-abelian Born-Infeld action including the tachyon potential for a stack of stable non-BPS branes on a critical orbifold. Finally we discuss stable soliton states on the non-BPS brane.
We discuss the physics of D-branes and D-brane instantons intersecting at angles, focusing on the (non)generation of a superpotential in the worldvolume theory of the branes. This is a short review of the results in arXiv:0905.1694, where we further emphasize both the macroscopic and microscopic structure of the manifestly supersymmetric instanton action. We also comment on the lift of O(1) instantons to F-theory.
We study cosmology on a BPS D3-brane evolving in the 10D SUGRA background describing a non-BPS brane. Initially the BPS brane is taken to be a probe whose dynamics we determine in the non-compact non-BPS background. The cosmology observed on the brane is of the FRW type with a scale factor $S(τ)$. In this mirage cosmology approach, there is no self-gravity on the brane which cannot inflate. Self-gravity is then included by compactifying the background space-time. The low energy effective theory below the compactification scale is shown to be bi-metric, with matter coupling to a different metri…
Following Sen's discovery of various stable non-BPS D-branes, K-theory has been shown to be the appropriate mathematical framework for classifying conserved D-brane charges. The classification accounts for known D-branes and predicts some new ones including a D8-brane in type I superstring theory. After briefly reviewing these developments, we discuss certain issues pertaining to the D8-brane, which is unstable.
The Green-Schwarz action for a non-BPS p=2 brane embedded in a N=1, D=4 target superspace is shown to be equivalent to the Nambu-Goto-Akulov-Volkov action obtained via the nonlinear realization of the associated target space super-Poincare symmetries. Introducing a U(1) gauge field strength as a Lagrange multiplier, this p=2 brane action is re-cast into its equivalent dual form non-BPS D2-brane Born-Infeld action. Following the procedure given by Sen, the Green-Schwarz action for a non-BPS D2-brane is determined directly. From it, conversely, the dual form non-BPS p=2 brane action is derived. …
We consider the open superstring action in the AdS$_4 \times \mathbf{CP}^3$ background and investigate the suitable boundary conditions for the open superstring describing the 1/2-BPS D-branes by imposing the $κ$-symmetry of the action. This results in the classification of 1/2-BPS D-branes from covariant open superstring. It is shown that the 1/2-BPS D-brane configurations are restricted considerably by the Kähler structure on $\mathbf{CP}^3$. We just consider D-branes without worldvolume fluxes.
The 1/8 BPS $D^6\mathcal{R}^4$ coupling in type II string theory compactified on $T^2$ receives contributions from worldsheet instantons and anti-instantons wrapping the $T^2$, up to genus three in string perturbation theory. These involve contributions separately from bound states of instantons and anti-instantons, which are qualitatively similar to such contributions to the 1/2 and 1/4 BPS couplings. At genus two, the $D^6\mathcal{R}^4$ coupling also receives contributions from instanton/anti-instanton bound states unlike the 1/2 and 1/4 BPS couplings, which is a consequence of a T-duality i…
We study the one-instanton sector of 5d U(N) maximal SYM theory. By using the moduli space approximation we obtain all the 1/4-BPS bound states of one dyonic instanton when a vev is given to one of the SYM scalar fields that breaks U(N) maximally. We compute the corresponding 1/4-BPS index and partition function and find agreement with arXiv:1110.2175.
As a step toward constructing realistic brane world models in string theory, we consider the interactions of a pair of non-BPS branes. We construct a dyonic generalization of the non-BPS branes first constructed by Bergman, Gaberdiel and Sen as orbifolds of D-branes on $T^4/\BZ_2$. The force between a dyonic brane and an electric brane is computed and is found to vanish at a nontrivial critical separation. This equilibrium point is unstable. For smaller separations the branes coalesce to form a composite dyonic state, while for larger separations the branes run off to infinity. We suggest gene…
Some time ago, Atiyah and Manton observed that computing the holonomy of Yang-Mills instantons yields good approximations to static Skyrmion solutions of the Skyrme model. This paper provides an extension and explanation of this result, by proving that instanton holonomies produce exact solutions of a BPS Skyrme model, in which the Skyrme field is coupled to a tower of vector mesons. Neglecting any (or indeed all) of the vector mesons breaks the scale invariance and removes the BPS property of the Skyrmions. However, it is shown that a truncation of the BPS Skyrme theory, in which only the fir…
We employ T-duality to restrict the tachyon dependence of effective actions for non-BPS D-branes. For the Born-Infeld part the criteria of T-duality and supersymmetry are satisfied by a simple extension of the D-brane Born-Infeld action.
We study the world-volume effective action of stable non-BPS branes present in Type II theories compactified on K3. In particular, by exploiting the conformal description of these objects available in the orbifold limit, we argue that their world-volume effective theory can be chiral. The resulting anomalies are cancelled through the usual inflow mechanism provided there are anomalous couplings, similar to those of BPS branes, to the twisted R-R fields. We also show that this result is in agreement with the conjectured interpretation of these non-BPS configurations as BPS branes wrapped on non…
Starting with the non-BPS D0-brane solution of IIB/$(-1)^{F_L}I_4$ constructed recently by Eyras and Panda we construct via T-duality the non-BPS D2-brane and D1-brane solutions of IIB/$(-1)^{F_L}I_4$ and IIA/$(-1)^{F_L}I_4$ predicted by Sen. The D2-brane couples magnetically to the vector field of the NS5B-brane living in the twisted sector of the Type IIB orbifold, whereas the D1-brane couples (electrically and magnetically) to the self-dual 2-form potential of the NS5A-brane that is present in the twisted sector of the Type IIA orbifold construction. Finally we discuss the eleven dimensiona…
We discuss the BPS configurations of IIB strings in the 7-brane background from M-theory viewpoint. We first obtain the hyperkahler geometry background of M-theory expected from the 7-brane solutions of the type IIB supergravity. We choose the appropriate complex structures of the background geometries and embed a membrane of M-theory holomorphically to obtain a BPS string configuration. The recently discussed BPS string configurations such as 3-string junctions and string networks in the flat background are generalized to the cases with the 7-brane backgrounds. The property of the BPS string …
We investigate an action which resembles the effective action of brane-antibrane system derived from boundary string field theory. We find that the action has smooth vortex solutions which saturate the Bogomol'nyi bound.
