Katrin Becker, Aaron Bergman
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.
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This note is devoted to the analysis of T-duality of Dp-brane when we perform T-duality along directions that are transverse to world-volume of Dp-brane.
We study D-brane actions in non-relativistic string theory. We consider single D-brane and analyse its properties under T-duality. We also derive an action for N D8-branes and also for lower dimensional D-branes through T-duality transformations.
We construct new type of non-relativistic D-branes which are defined with the help of T-duality along null direction. We find Lagrangian and Hamiltonian formulation of these D-branes and study their properties under T-duality transformations.
We show how the T-duality is realized for D-branes with noncommutative world-volume coordinates. We discuss D-branes wrapped on tori and the result is that the recently found noncommutative actions form a consistent collection due to the T-duality mapping between noncommutative D-branes and rotated commutative D-branes on deformed tori.
We discuss various dual {\it pairs} of $M$-theory compactifications. Each pair consists of a compactification in which the two-brane plays the crucial role in relation to a string theory and a compactification in which the five-brane takes center stage. We show that in many examples such dual pairs are interchanged by the {\it same} duality transformation in each case.
Extending earlier results on the duality symmetries of three-brane probe theories we define the duality subgroup of SL(2,Z) as the symmetry group of the background 7-branes configurations. We establish that the action of Weyl reflections is implemented on junctions by brane transpositions that amount to exchanging branes that can be connected by open strings. This enables us to characterize duality groups of brane configurations by a map to the symmetry group of the Dynkin diagram. We compute the duality groups and their actions for all localizable 7-brane configurations. Surprisingly, for the…
In this article the action of T-duality on a mixed brane is studied in the boundary state formalism. We also obtain a two dimensional mixed brane with non-zero electric and magnetic fields, from a D$_1$-brane.
We analyze the level-rank duality of omega_c-twisted D-branes of SU(N)_K (when N and K>2). When N or K is even, the duality map involves Z_2-cominimal equivalence classes of twisted D-branes. We prove the duality of the spectrum of an open string stretched between omega_c-twisted D-branes, and ascertain the relation between the charges of level-rank-dual omega_c-twisted D-branes.
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.
Level-rank duality of untwisted and twisted D-branes of WZW models is explored. We derive the relation between D0-brane charges of level-rank dual untwisted D-branes of su(N)_K and sp(n)_k, and of level-rank dual twisted D-branes of su(2n+1)_2k+1. The analysis of level-rank duality of twisted D-branes of su(2n+1)_2k+1 is facilitated by their close relation to untwisted D-branes of sp(n)_k. We also demonstrate level-rank duality of the spectrum of an open string stretched between untwisted or twisted D-branes in each of these cases.
Starting from the bosonic sector of the M-theory super-five-brane we obtain the action for duality-symmetric three-brane and construct the consistent coupling of the proposed action with the bosonic sector of type IIB supergravity.
When an NS5-brane crosses a D6-brane, a D4-brane is created stretching between them by the Hanany-Witten effect. However, the T-dual situation involves a Kaluza-Klein monopole crossing a D5-brane and should not result in brane creation. Thus, the newly created D4-brane disappears when T-duality is applied. The T-duality is in a direction transverse to the D4-brane so that one would naively have expected the creation of a D5-brane in the T-dual picture. This situation is investigated via the corresponding supergravity solutions and the tension with the naive result is resolved. Along the way, a…
We realize the string/$(D-5)$-brane duality on the action level between the $T^{10-D}$-compactified heterotic string effective action and the $(D-5)$- brane effective action in $D$ dimensions by managing a Lagrange multiplier field. A dual dictionary is composed to be available for the translation between the elementary or solitonic solutions of the dual pair of actions. In the same way the $S$ duality is also reconstructed on the action level as a double dualization for the $T^6$-compactified heterotic string effective action.
We compute the NSVZ beta functions for N = 1 four-dimensional quiver theories arising from D-brane probes on singularities, complete with anomalous dimensions, for a large set of phases in the corresponding duality tree. While these beta functions are zero for D-brane probes, they are non-zero in the presence of fractional branes. As a result there is a non-trivial RG behavior. We apply this running of gauge couplings to some toric singularities such as the cones over Hirzebruch and del Pezzo surfaces. We observe the emergence in string theory, of ``Duality Walls,'' a finite energy scale at wh…
We derive relations between type 0 and type II D-brane configurations under the T-duality suggested by Bergman and Gaberdiel and confirm that the massless fields on D-branes are identical to those on the dual D-brane configurations. Furthermore, we discuss dualities of type 0 and type II NS5-branes and find that the dual of an unwrapped type 0 NS5-brane is a Kaluza-Klein monopole with non-supersymmetric blow up modes.
Taking into account the recent dualities we rederive the super p-brane scan. Our main results are the importance of the metric's signature and the existence of an S self-dual super 5-brane at D=14 with signature (7,7) or (11,3).
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 show how the $T$--duality between $D$--branes is realized (i) on $p$--brane solutions $(p=0,\cdots ,9)$ of IIA/IIB supergravity and (ii) on the $D$--brane actions ($p=0,\cdots ,3)$ that act as source terms for the $p$--brane solutions. We point out that the presence of a cosmological constant in the IIA theory leads, by the requirement of gauge invariance, to a topological mass term for the worldvolume gauge field in the 2--brane case.
In this work an algorithm is proposed to calculate entropy for field theories living on NS five branes, which gives a result invariant under T-duality. This is a deformation of the well known Ryu-Takayanagi formula, which takes into account dependence of localized backgrounds for the branes on winding modes of strings.
The standard eleven-dimensional supergravity action depends on a three-form gauge field and does not allow direct coupling to five-branes. Using previously developed methods, we construct a covariant eleven-dimensional supergravity action depending on a three-form and six-form gauge field in a duality-symmetric manner. This action is coupled to both the M-theory two-brane and five-brane, and corresponding equations of motion are obtained. Consistent coupling relates D=11 duality properties with self-duality properties of the M-5-brane. From this duality-symmetric formulation, one can derive an…
We derive the super Yang-Mills action of Dp-branes on a torus T^{p-4} from the nonabelian (2,0) theory with Lie 3-algebra. Our realization is based on Lie 3-algebra with pairs of Lorentzian metric generators. The resultant theory then has negative norm modes, but it results in a unitary theory by setting VEV's of these modes. This procedure corresponds to the torus compactification, therefore by taking a transformation which is equivalent to T-duality, the Dp-brane action is obtained. We also study type IIA/IIB NS5-brane and Kaluza-Klein monopole systems by taking other VEV assignments. Such v…
We study T-duality transformations in canonical formalism for Nambu-Gotto action. Then we investigate the relation between world-sheet double Wick rotation and sequence of target space T-dualities and Wick rotation in case of fundamental string and D1-brane.
Following hep-th/0412336 we use the non-linear realisation of the semi-direct product of E11 and its vector representation to construct brane dynamics. The brane moves through a spacetime which arises in the non-linear realisation from the vector representation and it contains the usual embedding coordinates as well as the world volume fields. The resulting equations of motion are first order in derivatives and can be thought of as duality relations. Each brane carries the full E11 symmetry and so the Cremmer-Julia duality symmetries. We apply this theory to find the dynamics of the IIA and II…
We propose a construction of dual pairs in four dimensional N=1 supersymmetric Yang-Mills theory using branes in type IIA string theory.
We show that supersymmetric and $κ$-symmetric Dp-brane actions in type II supergravity background have the same duality transformation properties as those in a flat Minkowskian background. Specially, it is shown that the super D-string transforms in a covariant way while the super D3-brane is self-dual under the $SL(2,Z)$ duality. Also, the D2-brane and the D4-brane transform in ways expected from the relation between type IIA superstring theory and M-theory. The present study proves that various duality symmetries, which were originally found in the flat background field, are precisely valid …
A general black-branes system under the T-duality transformation will become another smeared system with different dimensional black branes. We first use some simple examples to see that both systems have a same value of entropy and then present a rigorous method to prove this general property. Using the property we could easily know the entropy of some complex black-brane systems.
The $D$-brane spectra in the Type IIB string theory compactified on $AdS_{p+2}\times S^{8-p}$ are computed using the K-theory approach. The results signal the existence of the mirror-symmetry-analogue for $D$-branes, analogous to that rised in the context of derived categories.
T-duality realized on D-brane effective actions is studied from a pure worldvolume point of view. It is proved that invariance in the form of the Dirac-Born-Infeld and Wess-Zumino terms fixes the T-duality transformations of the NS-NS and R-R background fields, respectively. The analysis is extended to uncover the mapping of global symmetries of the corresponding pair of D-branes involved in the transformation.
We study a new duality which pairs 4d N=1 supersymmetric quiver gauge theories. They are represented by brane tilings and are worldvolume theories of D3 branes at Calabi-Yau 3-fold singularities. The new duality identifies theories which have the same combined mesonic and baryonic moduli space, otherwise called the master space. We obtain the associated Hilbert series which encodes both the generators and defining relations of the moduli space. We illustrate our findings with a set of brane tilings that have reflexive toric diagrams.
Braneworld effective action for two-brane model is constructed by two different methods based respectively on the Dirichlet and Neumann boundary value problems. The equivalence of these methods is shown due to nontrivial duality relations between special boundary operators of these two problems.
We explicitly write down the invariant supersymmetry conditions for branes with generic values of moduli and U-duality charges in various space-time dimensions $D \leq 10$. We then use these results to obtain new BPS states, corresponding to network type structure of such branes.
We analyze the level-rank duality of untwisted and epsilon-twisted D-branes of the so(N)_K WZW model. Untwisted D-branes of so(N)_K are characterized by integrable tensor and spinor representations of so(N)_K. Level-rank duality maps untwisted so(N)_K D-branes corresponding to (equivalence classes of) tensor representations onto those of so(K)_N. The epsilon-twisted D-branes of so(2n)_2k are characterized by (a subset of) integrable tensor and spinor representations of so(2n-1)_2k+1. Level-rank duality maps spinor epsilon-twisted so(2n)_2k D-branes onto those of so(2k)_2n. For both untwisted a…
We derive level-rank duality in pure Chern-Simons gauge theories from a non-supersymmetric Seiberg duality by using a non-supersymmetric brane configuration in type IIB string theory. The brane configuration consists of fivebranes, N D3 antibranes and an O3 plane. By swapping the fivebranes we derive a 3d non-supersymmetric Seiberg duality. After level shifts from loop effects, this identifies the IR of Sp(2N)_{2k-2N+2} and Sp(2k-2N+2)_{-2N} pure Chern-Simons theories, which is a level-rank pair. We also derive level-rank duality in a Chern-Simons theory based on a unitary group.
T-duality (Fourier-Mukai duality) and properties of classical instanton moduli spaces can be used to deduce some properties of $α^{\prime}$-corrected moduli spaces of branes for Type IIA string theory compactified on $K3$ or $T^4$. Some interesting differences between the two compactifications are exhibited.
We propose a novel approach to the brane worldvolume theory based on the geometry of extended field theories: double field theory and exceptional field theory. We demonstrate the effectiveness of this approach by showing that one can reproduce the conventional bosonic string and membrane actions, and the M5-brane action in the weak-field approximation. At a glance, the proposed 5-brane action without approximation looks different from the known M5-brane actions, but it is consistent with the known nonlinear self-duality relation, and it may provide a new formulation of a single M5-brane action…
We show how the SL(5) duality in M-theory is explained from a canonical analysis of M2-brane mechanics. Diffeomorphism constraints for a M2-brane coupled to supergravity background in d=4 are reformulated in a SL(5) covariant form, in which spatial diffeomorphism constraints are recast into a SL(5) vector and the generalized metric in the Hamiltonian constraint is quartic in the SL(5) generalized vielbein. The Hamiltonian for a M2 brane has the SL(5) duality symmetry in a background dependent gauge.
Branes at a $\mathbb{F}_0$ singularity give rise to two different toric quiver gauge theories, which are related by Seiberg duality. We study where in the Kähler moduli space each of them is physically realized.
D-brane actions depend on a world-volume abelian vector field and are described by Born-Infeld-type actions. We consider the vector field duality transformations of these actions. Like the usual 2d scalar duality rotations of isometric string coordinates imply target space T-duality, this vector duality is intimately connected with SL(2,Z)-symmetry of type IIB superstring theory. We find that in parallel with generalised 4-dimensional Born-Infeld action, the action of 3-brane of type IIB theory is SL(2,Z) self-dual. This indicates that 3-brane should play a special role in type IIB theory and …
We construct the explicit worldvolume effective actions of the type IIB NS-5-brane and KK-monopole. These objects are obtained through a T-duality transformation from the IIA KK-monopole and the IIA NS-5-brane respectively. We show that the worldvolume field content of these actions is precisely that necessary to describe their worldvolume solitons. The IIB NS-5-brane effective action is shown to be related to the D-5-brane's by an S-duality transformation, suggesting the way to construct (p,q) 5-brane multiplets. The IIB KK-monopole is described by a gauged sigma model, in agreement with the …
We present a description of the type IIB NS-NS p-branes in terms of topological solitons in systems of spacetime-filling brane-antibrane pairs. S-duality implies that these spacetime-filling branes are NS9-branes, S-dual to the D9-branes of the type IIB theory. The possible vortex-like solutions in an NS9,anti-NS9 configuration are identified by looking at its worldvolume effective action. Finally we discuss the implications of these constructions in the description of BPS and non-BPS states in the strongly coupled Heterotic SO(32) theory.
We show that the fluxes of the various six-dimensional "gauge" theories are associated to below threshold bound states of D-branes with the NS-5-branes and KK-monopoles which preserve half of bulk supersymmetry. We then present the supergravity solutions that correspond to these bound states. In addition using the worldvolume solitons of IIA and IIB NS-5-branes and KK-monopoles, we investigate the sectors of the "gauge" theories that preserve one quarter of bulk supersymmetry. This leads to a generalization a supergravity solution which has the interpretation of two intersecting NS-5-branes at…
We study F-theory duals of heterotic line bundle models on elliptically fibered Calabi-Yau threefolds. These models necessarily contain NS5-branes which are geometrised in the dual F-theory compactifications. We initiate a systematic study of the correspondence between various configurations of NS5-branes and the dual geometries in F-theory and perform several checks of the duality. Furthermore, we discuss the singular transitions between different configurations of NS5-branes.
We show a duality of branes in the topological B-model by inserting two kinds of the non-compact branes simultaneously. We explicitly derive the integral formula for the matrix model partition function describing this situation, which correspondingly includes both of the characteristic polynomial and the external source. We show that these two descriptions are dual to each other through the Fourier transformation, and the brane partition function satisfies integrable equations in one and two dimensions.
A variant of the topological twist, involving SL(2,Z) dualities and hence named topological duality twist, is introduced and explicitly applied to describe a U(1) N=4 super Yang-Mills theory on a Kaehler space with holomorphically space-dependent coupling. Three-dimensional duality walls and two-dimensional chiral theories naturally enter the formulation of the duality twisted theory. Appropriately generalized, this theory is relevant for the study of Euclidean D3-brane instantons in F-theory compactifications. Some of its properties and implications are discussed.
We consider the left-right entanglement (LREE) entropy in 1+1 dimensions for WZW models on a circle, and for WZW models on untwisted and twisted D-branes. The consequences of level-rank duality for these applications is presented which provides a map of LREE from large to small central charge.
We describe a duality relation between configurations of M5-branes in M-theory and type IIB theory on Taub-NUT geometries with NSNS and RR 3-form field strength fluxes. The flux parameters are controlled by the angles between the M5-brane and the (T)duality directions. For one M5-brane, the duality leads to a family of supersymmetric flux configurations which interpolates between imaginary self-dual fluxes and fluxes similar to the Polchinski-Strassler kind. For multiple M5-branes, the IIB configurations are related to fluxes for twisted sector fields in orbifolds. The dual M5-brane picture al…
In extended supergravity theories there are $p$-brane solutions preserving different numbers of supersymmetries, depending on the charges, the spacetime dimension and the number of original supersymmetries (8, 16 or 32). We find U-duality invariant conditions on the quantized charges which specify the number of supersymmetries preserved with a particular charge configuration. These conditions relate U-duality invariants to the picture of intersecting branes. The analysis is carried out for all extended supergravities with 16 or 32 supersymmetries in various dimensions.
We show that the transformation of D-branes under T-duality on four-torus is represented by Nahm transform of instantons. The argument for this allows us to generalize Nahm transform to the case of orthogonal and symplectic gauge groups as well as to instantons on Z_2 orbifold of four-torus. In addition, we identify the isomorphism of K-theory groups that realizes the transformation of D-brane charges under T-duality on torus of arbitrary dimensions. By the isomorphism we are lead to identify the correct K-theory group that classifies D-brane charges in Type II orientifold.
The self-duality of Dirichlet $3$-brane action under the $SL(2,R)$ duality transformation of type IIB superstring theory is shown in the Hamiltonian form of the path integral for the partition function by performing the direct integration with respect to the boundary gauge field. Through the integration in the phase space the canonical momentum conjugate to the boundary gauge field can be effectively replaced by the dual gauge field.
We complete the classification of half-supersymmetric branes in toroidally compactified IIA/IIB string theory in terms of representations of the T-duality group. As a by-product we derive a last wrapping rule for the space-filling branes. We find examples of T-duality representations of branes in lower dimensions, suggested by supergravity, of which none of the component branes follow from the reduction of any brane in ten-dimensional IIA/IIB string theory. We discuss the constraints on the charges of half-supersymmetric branes, determining the corresponding T-duality and U-duality orbits.
The Wess-Zumino coupling on D-branes in string theory is known to receive higher derivative corrections which couple the Ramond-Ramond potential to terms involving the square of the spacetime curvature tensor. Consistency with T-duality implies that the branes should also have four-derivative couplings that involve the NS-NS B-field. We use T-duality to predict some of these couplings. We then confirm these results with string worldsheet computations by evaluating disc amplitudes with insertions of one R-R and two NS-NS vertex operators.
It has been claimed that whereas scalars can be bound to a Randall-Sundrum brane, higher p-form potentials cannot, in contradiction with the Hodge duality between 0-form and 3-form potentials in the five-dimensional bulk. Here we show that a 3-form in the bulk correctly yields a 2-form on the brane, in complete agreement with both bulk and brane duality. We also emphasize that the phenomenon of photon screening in the Randall-Sundrum geometry is ruled out by the bulk Einstein equation.
We derive the stability conditions for the M5-brane in topological M-theory using kappa-symmetry. The non-linearly self-dual 3-form on the world-volume is necessarily non-vanishing, as is the case also for the 2-form field strengths on coisotropic branes in topological string theory. It is demonstrated that the self-duality is consistent with the stability conditions, which are solved locally in terms of a tensor in the representation 6 of SU(3) in G_2. The double dimensional reduction of the M5-brane is the D4-brane, and its direct reduction is an NS5-brane. We show that the equation of motio…
T-duality realized on SuperD-brane effective actions probing in constant $G_{mn}$ and $b_{mn}$ backgrounds is studied from a pure world volume point of view. It is proved that requiring {\em T-duality covariance} of such actions ``fixes'' the T-duality transformations of the world volume dynamical fields, and consequently, of the NS-NS and R-R coupling superfields. The analysis is extended to uncover the mapping of the symmetry structure associated with these SuperD-brane actions. In particular, we determine the T-duality transformation properties of kappa symmetry and supersymmetry, which all…
We establish self-duality of super D3-brane theory as an exact symmetry of the action both in the Lagrangian and Hamiltonian formalism. In the Lagrangian formalism, the action is shown to satisfy the Gaillard-Zumino condition. This algebraic relation is recognized in our previous paper to be a necessary and sufficient condition for generic action of U(1) gauge field strength coupled with gravity and matters to be self-dual. For the super D3-brane action, SO(2) duality transformation of a world-volume gauge field should be associated with SO(2) rotation of fermionic brane coordinates in N=2 SUS…
We propose a method for constructing super-brane actions where every background tensor potential corresponds to a world-volume field strength. The procedure provides a natural coupling to the background and automatically displays the SL(2;Z) symmetry of the IIB string theory. The Dirichlet 3-brane is used as a test ground for these ideas. A polynomial action consistent with non-linear self-duality is presented. Invariance of the action under kappa-symmetry is demonstrated for arbitrary on-shell type IIB supergravity backgrounds and is shown to require self-duality.
We study a special combination of the compact directions of the spacetime (compactified on tori) and the worldsheet parity transformed of these directions. The transformations that change the compact part of the spacetime to this combination, are more general than the T-duality transformations. Many properties of this combination and also of the corresponding worldsheet fermions are studied. By using the boundary state formalism, we study the effects of the above transformations to D-branes. For the special cases the resulted branes reduce to the known mixed branes, or reduce to the modified m…
We examine the known curvature terms in the DBI part of the D-brane action under the T-duality transformation. Using the compatibility of the action with the standard rules of T-duality at the linear order as a guiding principle, we include the appropriate NS-NS $B$-field terms in the action and show that they reproduce the O(α'^2) terms of the corresponding disk-level scattering amplitude.
We use field theory and brane diamond techniques to demonstrate that Toric Duality is Seiberg duality for N=1 theories with toric moduli spaces. This resolves the puzzle concerning the physical meaning of Toric Duality as proposed in our earlier work. Furthermore, using this strong connection we arrive at three new phases which can not be thus far obtained by the so-called ``Inverse Algorithm'' applied to partial resolution of C^3/Z_3 x Z_3. The standing proposals of Seiberg duality as diamond duality in the work by Aganagic-Karch-Lüst-Miemiec are strongly supported and new diamond configurati…
The consequences of level-rank duality for untwisted D-branes on an SU(N) group manifold are explored. Relations are found between the charges of D-branes (which are classified by twisted K-theory) belonging to su(N)_K and su(K)_N WZW theories, in the case of odd N+K. An isomorphism between the charge algebras is also demonstrated in this case.
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