We compute the four-dimensional gaugino mass for a Dp-brane extended in spacetime and wrapping a cycle on the internal geometry in a warped compactification with fluxes. Motivated by the backreaction of gaugino bilinear VEVs, we use Generalized Complex Geometry to characterize the internal geometry as well as the cycle wrapped by the brane. We find that the RR fluxes and the non-closure of the generalized complex structures combine in the gaugino mass terms in the same form as they do in the bulk superpotential, while for the NSNS fluxes there is a crucial minus sign in the component normal to the brane. Our expression extends the known result for D3 and D7-branes in Calabi-Yau manifolds, where the gaugino masses are induced respectively by the imaginary anti-self dual and imaginary self-dual components of the complex 3-form flux $G_3$.
We present the potential energy due to flux and gaugino condensation in heterotic M-theory compactifications with anti-branes in the vacuum. For reasons which we explain in detail, the contributions to the potential due to flux are not modified from those in supersymmetric contexts. The discussion of gaugino condensation is, however, changed by the presence of anti-branes. We show how a careful microscopic analysis of the system allows us to use standard results in supersymmetric gauge theory in describing such effects - despite the explicit supersymmetry breaking which is present. Not surpris…
We investigate, at the microscopic level, the compatibility between D-term potentials from world-volume fluxes on D7-branes and non-perturbative superpotentials arising from gaugino condensation on a different stack of D7-branes. This is motivated by attempts to construct metastable de Sitter vacua in type IIB string theory via D-term uplifts. We find a condition under which the Kaehler modulus, T, of a Calabi-Yau 4-cycle gets charged under the anomalous U(1) on the branes with flux. If in addition this 4-cycle is wrapped by a stack of D7-branes on which gaugino condensation takes place, the q…
We consider the brane-localized supersymmetry breaking in 5D compactified on $S^1/Z_2$. In case of a bulk gaugino with arbitrary brane masses for its even and odd modes, we find the mass spectrum and the wave functions of gaugino. We show that the gaugino masses at the distant brane are soft in the usual sense in the effective field theory with zero modes of bulk gauge fields and they are also extremely soft in view of the one-loop finite mass of a brane scalar in the KK regularization.
Gaugino condensation plays a crucial role in the formation of dS vacua. However, the theory of this effect is still incomplete. In 4d the perfect square nature of gaugino couplings follows from the square of auxiliaries in the supergravity action. We explain here why the supersymmetric non-Abelian Dp-brane action, which is the basis for the theory of 10d gaugino condensation, must have a 4-gaugino coupling. This term in the Einstein-Yang-Mills 10d supergravity is a part of the perfect square, mixing a 3-form with gaugino bilinear. The perfect square term follows from the superspace geometry, b…
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.
There are two known sources of nonperturbative superpotentials for Kähler moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The first class of effects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the fourfold, is relatively well understood. The second class has been less explored. In this paper, we consider the explicit example of F-theory on $K3 \times K3$ with flux. The fluxes lift the D7 brane matter fields, an…
We review progress in studying the solutions of SQCD in the presence of explicit, soft SUSY breaking terms. Massive N=1 SQCD in the presence of a small gaugino mass leads to a controlled solution which has interesting phase structure with changing theta angle reminiscent of the QCD chiral Lagrangian. Current attempts to test the solutions of pure glue SQCD on the lattice require a theoretical understanding of the theory with small gaugino mass in order to understand the approach to the SUSY point. We provide such a description making predictions for the gaugino condensate and lightest bound st…
We analyze the structure of gaugino interactions on D7-branes from a 10d perspective. This is essential if one wants to lift the standard 4d approach to type IIB moduli stabilization to 10d. In particular, a 10d picture has recently been used to raise concerns about the KKLT proposal for constructing de Sitter vacua, and to lend support to swampland conjectures against de Sitter. However, the analyses of brane gaugino condensation so far are plagued by UV divergences and do not include local 4-fermion terms. They also fail to reproduce the 4-fermion terms required by supergravity when compacti…
Coupling of bilinears of gauginos on D-branes to anti-symmetric tensor fields can be deduced by comparing F-theory compactified to 8 dimensions with the heterotic string on $R^8\times T^2$. Application to SUSY breaking in F-theory triggered by gaugino condensation is discussed. Compactification to four dimensions with a warp factor is briefly discussed. In this case some 3-branes whose world-volume coincides with the open spacetime must be introduced, in addition to 7-branes.
Within the ongoing debate about de Sitter (dS) vacua in string theory, different aspects of explicit dS proposals have come under intense scrutiny. One key ingredient is D7-brane gaugino condensation, which is usually treated using effective 4d supergravity. However, it is clearly more desirable to derive the relevant scalar potential directly from a local 10d Lagrangian. Such a local 10d description captures the interactions among the various localized sources and the background fields which are smeared in the 4d Lagrangian. While progress in this endeavour has recently been made, some form o…
We describe the back-reaction of gaugino condensates in supersymmetric AdS$_4$ Type II String Theory compactifications with fluxes. We use generalized complex geometry to capture the modification of the ten-dimensional supersymmetry equations and show that the cosmological constant prevents the cycle wrapped by the branes with gaugino condensation from shrinking to zero size. Thus, unlike in ordinary geometric transitions in flat space, the volume of this cycle remains finite. For D7 branes with gaugino condensation, this gives a ten-dimensional account of Kähler moduli stabilization. Furtherm…
We propose a mechanism for mediating supersymmetry breaking in Type I string constructions. The basic set-up consists of a system of three D-branes: two parallel D-branes, a matter D-brane and a source D-brane, with supersymmetry breaking communicated via a third D-brane, the mediating D-brane, which intersects both of the parallel D-branes. We discuss an example in which the first and second family matter fields correspond to open strings living on the intersection of the matter D-brane and mediating D-brane, while the gauge fields, Higgs doublets and third family matter fields correspond to …
Gaugino condensation on D-branes wrapping internal cycles gives a mechanism to stabilize the associated moduli. According to the effective field theory, this gives rise, when combined with fluxes, to supersymmetric AdS$_4$ solutions. In this paper we provide a ten-dimensional description of these vacua. We first find the supersymmetry equations for type II AdS$_4$ vacua with gaugino condensates on D-branes, in the framework of generalized complex geometry. We then solve them for type IIB compactifications with gaugino condensates on smeared D7-branes. We show that supersymmetry requires a (con…
We study anomaly mediated supersymmetry breaking in type IIB string theory and use our results to test the supergravity formula for anomaly mediated gaugino masses. We compute 1-loop gaugino masses for models of D3-branes on orbifold singularities with 3-form fluxes by calculating the annulus correlator of 3-form flux and two gauginos in the zero momentum limit. Consistent with supergravity expectations we find both anomalous and running contributions to 1-loop gaugino masses. For background Neveu-Schwarz H-flux we find an exact match with the supergravity formula. For Ramond-Ramond flux there…
I consider supergravity solutions of D5 branes wrapped on supersymmetric 2-cycles and use them to discuss relevant features of four-dimensional N=1 super Yang-Mills theories with gauge group SU(N). In particular, using a gravitational dual of the gaugino condensate, it is shown that is possible to obtain the complete NSVZ $β$-function. It is also described how different aspects of the gauge theory are nicely encoded in this supergravity solution.
We study non-supersymmetric SO(3)-invariant deformations of d=3, N=8 super Yang-Mills theory and their type IIA string theory dual. By adding both gaugino mass and scalar mass, dielectric D4-brane potential coincides with D5-brane potential in type IIB theory. We find the region of parameter space where the non-supersymmetric vacuum is described by stable dielectric NS5-branes. By considering the generalized action for NS5-branes in the presence of D4-flux, we also analyze the properties of dielectric NS5-branes.
Recently the construction of the non-abelian effective D-brane action was performed through order $α'{}^3$ including the terms quadratic in the gauginos. This result can be tested by calculating the spectrum in the presence of constant magnetic background fields and comparing it to the string theoretic predictions. This test was already performed for the purely bosonic terms. In this note we extend the test to the fermionic terms. We obtain perfect agreement.
In D-brane models, different part of the 4-dimensional gauge group might originate from D-branes wrapping different cycles in the internal space, and then the standard model gauge couplings at the compactification scale are determined by different cycle-volume moduli. We point out that those cycle-volume moduli can naturally have universal vacuum expectation values up to small deviations suppressed by 1/8π^2 if they are stabilized by KKLT-type non-perturbative superpotential. This dynamical unification of gauge couplings is independent of the detailed form of the moduli Kähler potential, but r…
We discuss string corrections to the effective potential in various models of brane inflation. These corrections contribute to the mass of the inflaton candidate and may improve its slow-roll properties. In particular, in orientifold string compactifications with dynamical D3- and D7-branes, the corrections induce inflaton dependence in the part of the superpotential that arises from gaugino condensation or other nonperturbative effects. The additional terms are in part required by supersymmetry. We explicitly discuss D3/D7-inflation, where flat directions of the potential can be lifted, and t…
We consider supergravity solutions of D5 branes wrapped on supersymmetric 2-cycles and use them to discuss relevant features of four-dimensional N=1 and N=2 super Yang-Mills theories with gauge group SU(n). In particular in the N=1 case, using a gravitational dual of the gaugino condensate, we obtain the complete NSVZ beta-function. We also find non-perturbative corrections associated to fractional instantons with charge 2/n. These non-perturbative effects modify the running of the coupling constant which remains finite even at small scales in a way that resembles to the soft confinement scena…
In type IIB large volume compactifications involving orientifolds of the Swiss-Cheese Calabi-Yau [11169] with a single mobile space-time filling D3-brane and stacks of D7-branes wrapping the "big" divisor (D_5) and supporting D7-brane fluxes, (i) using the toric data and GLSM techniques, we obtain the geometric Kaehler potential for D_5 in terms of genus-two Siegel theta functions; (ii) we show that as the D3-brane moves from a particular embedded non-singular elliptic curve to another one, it is possible to obtain 10^{12}GeV gravitino during the inflationary era as well as a TeV gravitino in …
We derive various solutions for the gauge field and the gaugino when there are both 5D bulk kinetic terms and 4D brane kinetic terms. Below the compactification scale $1/y_c$, gauge interaction by the massless mode is universal, independent of the locations of sources, but above $1/y_c$, the interaction distinguishes their locations. We consider the $S^1/(Z_2\times Z_2')$ orbifold compactification, in which N=2 SUSY and SU(2) gauge symmetry break down to N=1 and U(1), respectively. While the odd parity gauge fields under $Z_2$, $A^1_μ$ and $A^2_μ$, interact with the bulk gauge coupling $g^2$, …
We discuss the moduli-dependent couplings of the higher derivative F-terms $(\Tr W^2)^{h-1}$, where $W$ is the gauge N=1 chiral superfield. They are determined by the genus zero topological partition function $F^{(0,h)}$, on a world-sheet with $h$ boundaries. By string duality, these terms are also related to heterotic topological amplitudes studied in the past, with the topological twist applied only in the left-moving supersymmetric sector of the internal $N=(2,0)$ superconformal field theory. The holomorphic anomaly of these couplings relates them to terms of the form $Π^n({\rm Tr}W^2)^{h-2…
We study worldsheet instanton corrections to the exotic 522-brane geometry in type II string theory. The BPS vortices in the N=(4,4) gauged linear sigma model modify the geometry of the 522-brane. We find that the modification of the geometry is understood by the localization in the T-dualized winding direction.
We study non-supersymmetric orbifold singularities from the point of view of D-brane probes. We present a description of the decay of such singularities from considerations of the toric geometry of the probe branes.
In this paper, we give a map from matrices to a commutative geometry from a bound state of a D2-brane and N D0-branes. For this, tachyons in auxiliary unstable D-brane system describing the bound state play crucial roles. We found the map obtained in this way coincides with the recent proposals. We also consider the map from the geometry to matrices in a large N limit and argue that the map is a matrix regularization of geometry.
We use toric geometry to investigate the recently proposed relation between a set of D3 branes at a generalized conifold singularity and type IIA configurations of D4 branes stretched between a number of relatively rotated NS5 branes. In particular we investigate how various resolutions of the singularity corresponds to moving the NS branes and how Seiberg's duality is realized when two relatively rotated NS-branes are interchanged.
We have analyzed the interplay between Scherk-Schwarz supersymmetry breaking and general fermion (gaugino or gravitino) mass terms localized on the fixed point branes of the S^1/Z_2 orbifold. Analytic solutions for eigenfunctions and eigenvalues are found in all cases. All results are checked by numerical calculations that make use of regularized δ-functions. Odd and generically also even fermions are discontinuous at the brane fixed points, but in all cases the combination that couples to the brane is continuous. For CP-even brane mass terms supersymmetry restoration can take place when their…
We show that in a general hidden sector model, supersymmetry breaking necessarily generates at one-loop a scalar and gaugino mass as a consequence of the super-Weyl anomaly. We study a scenario in which this contribution dominates. We consider the Standard Model particles to be localized on a (3+1)-dimensional subspace or ``3-brane'' of a higher dimensional spacetime, while supersymmetry breaking occurs off the 3-brane, either in the bulk or on another 3-brane. At least one extra dimension is assumed to be compactified roughly one to two orders of magnitude below the four-dimensional Planck sc…
We show that toric geometry can be used rather effectively to translate a brane configuration to geometry. Roughly speaking the skeletons of toric space are identified with the brane configurations. The cases where the local geometry involves hypersurfaces in toric varieties (such as P^2 blown up at more than 3 points) presents a challenge for the brane picture. We also find a simple physical explanation of Batyrev's construction of mirror pairs of Calabi-Yau manifolds using T-duality.
Coset models and their symmetry preserving branes are studied from a representation theoretic perspective, relating e.g. the horizontal branching spaces to a truncation of the space of bulk fields, and accounting for field identification. This allows us to describe the fuzzy geometry of the branes at finite level.
We discuss the nonabelian world-volume action which governs the dynamics of N coincident Dp-branes. In this theory, the branes' transverse displacements are described by matrix-valued scalar fields, and so this is a natural physical framework for the appearance of noncommutative geometry. One example is the dielectric effect by which Dp-branes may be polarized into a noncommutative geometry by external fields. Another example is the appearance of noncommutative geometries in the description of intersecting D-branes of differing dimensions, such as D-strings ending on a D3- or D5-brane. We also…
A D3 brane in the background of NS5 branes is studied semi-classically. The conditions for preserved supersymmetry are derived, leading to a differential equation for the shape of the D3 brane. The solutions of this equation are analyzed. For a D3 brane intersecting the NS5 branes, the angle of approach is known to be restricted to discrete values. Four different ways to obtain this quantization are described. In particular, it is shown that, assuming the D3 brane avoids intersecting a {\em single} NS5 brane, the above discrete values correspond to the different possible positions of the D3 br…
Starting from the usual bosonic membrane action, we develop the geometry suitable for the description of $p$-brane backgrounds. Using the tools of generalized geometry we derive the generalization of string open-closed relations. Nambu-Poisson structures are used to generalize the concept of semiclassical noncommutativity of $D$-branes governed by Poisson tensor. We naturally describe the correspondence of recently proposed commutative and noncommutative versions of an effective action for $p$-branes ending on a $p'$-brane. We calculate the power series expansion of the action in background in…
In this note we analyze the geometry of maximally symmetric boundary conditions in Lie supergroup Wess-Zumino-Novikov-Witten models. We find that generically the worldvolume of a brane is a twisted superconjugacy class, very much like in the Lie group case. Whenever the brane is not completely delocalized in the fermionic directions a new atypical class of branes arises. We give an example of these new branes and show for type I supergroups and trivial gluing conditions that they can be naturally associated with atypical representations of the affine Lie superalgebra.
We introduce a Nambu-Poisson bracket in the geometrical description of the D=11 M5-brane. This procedure allows us, under some assumptions, to eliminate the local degrees of freedom of the antisymmetric field in the M5-brane Hamiltonian and to express it as a D=11 p-brane theory invariant under symplectomorphisms. A regularization of the M5-brane in terms of a multi D1-brane theory invariant under the $SU(N)\times SU(N)$ group in the limit when $N\to\infty$ is proposed. Also, a regularization for the D=10 D4-brane in terms of a multi D0-brane theory is suggested.
For supersymmetric solutions of D3(M2) branes with AdS3(AdS2) factor, it is known that the internal space is expressible as U(1) fibration over Kähler space which satisfies a specific partial differential equation involving the Ricci tensor. In this paper we study the wrapped brane solutions of D3 and M2-branes which were originally constructed using gauged supergravity and uplifted to D=10 and D=11. We rewrite the solutions in canonical form, identify the backreacted Kähler geometry, and present a class of solutions which satisfy the Killing spinor equation.
The disk partition function of the open topological string computes the spacetime superpotential for D-branes wrapping cycles of a compact Calabi-Yau threefold. We use string duality to show that when appropriately formulated, the problem admits a natural geometrization in terms of a non-compact Calabi-Yau fourfold without D-branes. The duality relates the D-brane superpotential to a flux superpotential on the fourfold. This sheds light on several features of superpotential computations appearing in the literature, in particular on the observation that Calabi-Yau fourfold geometry enters the p…
Our motivation is to find the relationship between the commutator of coordinates and uncertainty relation involving only the coordinates. The boundary condition with constant background field is connected with the rotation of D-brane at general angle. And the mode expansions of D-brane we found is more reasonable than those appeared in literature. The partition functions and scattering amplitudes are also discussed.
The characterization of the DBI action of a Dp-brane using the generalized geometry is discussed. It is shown that the DBI action is invariant under the diffeomorphism and B-transformation of the generalized tangent bundle of the target space. The symmetry is realized non-linearly on the fluctuation of the D-brane.
In this article, we study how the Grothendieck group of coherent sheaves can be used to describe D-branes. We show how global bound state construction in topological $K$-theory can be adapted to our context, showing that D-branes wrapping a subvariety are holomorphically classified by a relative $K$-group. By taking the duality between the relative $K$-groups and the $K$-homologies, we show that D-brane charge of type IIB superstrings is properly classified by the $K$-homology.
We consider string theory on the Lorentzian Melvin geometry, which is obtained by analytically continuing the two-parameter Euclidean Melvin background. Because this model provides a solvable conformal field theory that describes time-dependent twisted string dynamics, we study the string one-loop partition function and the D-brane spectrum. We found that both the wrapping D2-brane and the codimension-one D-string emit winding strings, and this behavior can be traced to the modified open string Hamiltonian on these probe D-branes.
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…
Using properties of the DBI action we find D-branes on $S^3$ of the radius $Q_5$ corresponding to the conjugacy classes of SU(2). The branes are stable due to nonzero 2-form NSNS background. In the limit of large $Q_5$ the dynamics of branes is governed by the non-commutative Yang-Mills theory. The results partially overlap with those obtained in the recent paper hep-th/0003037.
We find explicit solutions of Type IIB string theory on R^4/Z_2 corresponding to the classical geometry of fractional D1-branes. From the supergravity solution obtained, we capture perturbative information about the running of the coupling constant and the metric on the moduli space of N=4, D=2 Super Yang Mills.
We show how non-compact (quantum 2d AdS) space-time emerges for specific ratios of the square of the boundary cosmological constant to the cosmological constant in 2d Euclidean quantum gravity.
Basic idea of Randall-Sundrum brane world model I and II is reviewed with detailed calculation. After introducing the brane world metric with exponential warp factor, metrics of Randall-Sundrum models are constructed. We explain how Randall-Sundrum model I with two branes makes the gauge hierarchy problem much milder, and then derive Newtonian gravity in Randall-Sundrum model II with a single brane by considering small fluctuations.
We characterize the geometry produced by M5-branes wrapping a Special Lagrangian 3-cycle in a Calabi-Yau 3-fold. The presence of the brane replaces the the Calabi-Yau by a real manifold with an almost complex structure. We show that, in this classification, a distinguished (1,1) form as well as a globally defined (3,0) form play an important role. The requirements of supersymmetry preservation impose constraints on these structures which can be used to classify the background.
We report on the gauged supergravity analysis of Type IIB vacua on K3x T2/Z2 orientifold in the presence of D3-D7-branes and fluxes. We discuss supersymmetric critical points correspond to Minkowski vacua and the related fixing of moduli, finding agreement with previous analysis. An important role is played by the choice of the symplectic holomorphic sections of special geometry which enter the computation of the scalar potential. The related period matrix N is explicitly given. The relation between the special geometry and the Born--Infeld action for the brane moduli is elucidated.
By looking at fractional Dp-branes of type IIA on T_4/Z_2 as wrapped branes and by using boundary state techniques we construct the effective low-energy action for the fields generated by fractional branes, build their world-volume action and find the corresponding classical geometry. The explicit form of the classical background is consistent only outside an enhancon sphere of radius r_e, which encloses a naked singularity of repulson-type. The perturbative running of the gauge coupling constant, dictated by the NS-NS twisted field that keeps its one-loop expression at any distance, also fail…
We investigate the open string modes, describing the world-volume of a D p-brane, for its cyclic symmetry in presence of a magnetic field. It is argued that the constant coordinate modes receive non-perturbative correction. We show that they introduce the notion of noncommutativity on the D p-brane world-volume and make it UV-renormalizable. An analogy between cyclic symmetry ($\a'$-corrections) and the noncommutative geometry ($Θ_A$-corrections) is presented to explain some of the unusual IR phenomena often noticed in a noncommutative theory.
Branes in non-trivial backgrounds are expected to exhibit interesting dynamical properties. We use the boundary conformal field theory approach to study branes in a curved background with non-vanishing Neveu-Schwarz 3-form field strength. For branes on an $S^3$, the low-energy effective action is computed to leading order in the string tension. It turns out to be a field theory on a non-commutative `fuzzy 2-sphere' which consists of a Yang-Mills and a Chern-Simons term. We find a certain set of classical solutions that have no analogue for flat branes in Euclidean space. These solutions show, …
We study the geometry of M5-branes wrapping a 2-cycle which is Special Lagrangian with respect to a specific complex structure in a Calabi-Yau two-fold. Using methods recently applied to the three-fold case, we are again able find a characterization of the geometry, in terms of a non-integrable almost complex structure and a (2,0) form. This time, however, due to the hyper-K{ä}hler nature of the underlying 2-fold we also have the freedom of choosing a different almost complex structure with respect to which the wrapped 2-cycle is holomorphic. We show that this latter almost complex structure i…
We consider a novel scenario for modulus stabilisation in IIB string compactifications in which the Kahler moduli are stabilised by a general set-up with two kinds of non-perturbative effects: (i) standard Kahler moduli-dependent non-perturbative effects from gaugino condensation on D7-branes or E3-instantons wrapping four-cycles in the geometric regime; (ii) dilaton-dependent non-perturbative effects from gaugino condensation on space-time filling D3-branes or E(-1)-instantons at singularities. For the LARGE Volume Scenario (LVS), the new dilaton-dependent non-perturbative effects provide a p…
We show that the Nahm equation which describes a fuzzy D3-brane in the presence of a B-field can be derived as a boundary condition of the F1-strings ending on the D3-brane, and that the modifications of the original Nahm equation by a B-field can be understood in terms of the noncommutative geometry of the D3-brane. Naturally this is consistent with the alternative derivation by quantising the open strings in the B-field background. We then consider a configuration of multiple M2-branes ending on an M5-brane with a constant 3-form C-field. By analogy with the case of strings ending on a D3-br…
We investigate boundary states of D-branes wrapped around supersymmetric cycles in Kazama--Suzuki models. We show that the geometry of the D-branes corresponds to a generalisation of calibrated geometry. We comment on the link with the geometry of the coset space and discuss how T-duality maps between these boundary states.
We analyze behaviour of D3-branes in BGMPZ throat geometry. We show that although single brane has some of the moduli stabilized multi-brane system tends to expand and form a bound state. Such a system loses non-abelian gauge symmetry.
