Tetiana Obikhod, Ievgenii Petrenko
The paper is connected with searches for the Ramond-Ramond charge of D branes in the presence of B field. The consideration of B field inclusion is an important physical and mathematical unsolved problem, which is connected with K group calculations of twisted bundles. Considered two cases of vector bundles, Azumaya and Rosenberg algebras and analyzed their K group realization.
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We consider configurations of D6-branes with D0-brane charge given by recent work of Taylor and compute interaction potentials with various D-brane probes using a 1-loop open string calculation. These results are compared to a supergravity calculation using the solution given by Sheinblatt of an extremal black hole carrying 0-brane and 6-brane charge.
We discuss the discrete Z_k D-brane charges (twisted K-theory charges) in five-brane backgrounds from several different points of view. In particular, we interpret it as a result of a standard Higgs mechanism. We show that certain degrees of freedom (singletons) on the boundary of space can extend the corresponding Z_k symmetry to U(1). Related ideas clarify the role of AdS singletons in the AdS/CFT correspondence.
In axion monodromy inflation, traversing $N$ axion periods corresponds to discharging $N$ units of a quantized charge. In certain models with moving D7-branes, such as Higgs-otic inflation, this monodromy charge is D3-brane charge induced on the D7-branes. The stress-energy of the induced charge affects the internal space, changing the inflaton potential and potentially limiting the field range. We compute the backreaction of induced D3-brane charge in Higgs-otic inflation. The effect on the nonperturbative superpotential is dramatic even for $N=1$, and may preclude large-field inflation in th…
The charges of the twisted D-branes of certain WZW models are determined. The twisted D-branes are labelled by twisted representations of the affine algebra, and their charge is simply the ground state multiplicity of the twisted representation. It is shown that the resulting charge group is isomorphic to the charge group of the untwisted branes, as had been anticipated from a K-theory calculation. Our arguments rely on a number of non-trivial Lie theoretic identities.
The known extended algebras associated with p-branes are shown to be generated as topological charge algebras of the standard p-brane actions. A representation of the charges in terms of superspace forms is constructed. The charges are shown to be the same in standard/extended superspace formulations of the action.
We derive general equations which determine the decomposition of the G^{+++} multiplet of brane charges into the sub-algebras that arise when the non-linearly realised G^{+++} theory is dimensionally reduced on a torus. We apply this to calculate the low level E_8 multiplets of brane charges that arise when the E_{8}^{+++}, or E_{11}, non-linearly realised theory is dimensionally reduced to three dimensions on an eight dimensional torus. We find precise agreement with the U-duality multiplet of brane charges previously calculated, thus providing a natural eleven dimensional origin for the "mys…
The charges of the twisted D-branes for the two exceptional cases (SO(8) with the triality automorphism and E_6 with charge conjugation) are determined. To this end the corresponding NIM-reps are expressed in terms of the fusion rules of the invariant subalgebras. As expected the charge groups are found to agree with those characterising the untwisted branes.
The charges of the twisted branes for strings on the group manifold SU(n)/Z_d are determined. To this end we derive explicit (and remarkably simple) formulae for the relevant NIM-rep coefficients. The charge groups of the twisted and untwisted branes are compared and found to agree for the cases we consider.
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.
It is argued that D-brane charge takes values in K-homology. For smooth manifolds with spin structure, this could explain why the phase factor $Ω(x)$ calculated with a D-brane state x in IIB theory appears in Diaconescu, Moore and Witten's computation of the partition function of IIA string theory.
We compute RR charges of D2-branes on a background with H-field which belongs to a nontrivial cohomology class. We discover that the RR charge depends on the configuration of the background `electric' RR field. This result explains the ambiguity in the definition of the RR charge previously observed in the SU(2) WZW model.
The Green-Siegel central extension of superalgebras for BPS branes is studied. In these cases commutators of usual bosonic brane charges only with the broken supersymmetry charges allow this central extension. We present an interpretation of these fermionic central charges as fermionic brane charges, and show that they take nonzero values for a nontrivial fermionic boundary condition. Such fermionic coordinates solutions are determined by equations of motion in a suitable gauge condition which manifests Nambu-Goldstone fermionic modes as well as bosonic modes in the static gauge. We also show …
We argue that a modification of the super-AdS algebras which accounts for the presence of D-branes requires not only the inclusion of bosonic brane charges, but also the inclusion of new fermionic ones. We show that such fermionic brane charges are indeed present in the matrix model and the supermembrane in the pp-wave limit of the corresponding backgrounds. We briefly comment on an AdS version of Sezgin's M-algebra inspired by this observation.
We show that the central charge of the Liouville and ADE Toda theories can be reproduced by equivariantly integrating the anomaly eight-form of the corresponding six-dimensional N=(0,2) theories, which describe the low-energy dynamics of M5-branes.
We consider the contribution of the B-field into the RR charge of a spherical D2-brane. Extending a recent analysis of Taylor, we show that the boundary and bulk contributions do not cancel in general. Instead, they add up to an integer as observed by Stanciu. The general formula is applied to compute the RR charges of spherical D-branes of the SU(2) WZW model at level k and it shows that these RR charges are only defined modulo k+2. We support this claim by studying bound state formation of D0-branes using boundary conformal field theory.
We investigate orientifold of brane tilings. We clarify how the cancellations of gauge anomaly and Witten's anomaly are guaranteed by the conservation of the D5-brane charge. We also discuss the relation between brane tilings and the dual Calabi-Yau cones realized as the moduli spaces of gauge theories. Two types of flavor D5-branes in brane tilings and corresponding superpotentials of fundamental quark fields are proposed, and it is shown that the massless loci of these quarks in the moduli space correctly reproduce the worldvolume of flavor D7-branes in the Calabi-Yau cone dual to the fivebr…
We investigate the evolution of small perturbations around charged black strings and branes which are solutions of low energy string theory. We give the details of the analysis for the uncharged case which was summarized in a previous paper. We extend the analysis to the small charge case and give also an analysis for the generic case, following the behavior of unstable modes as the charge is modified. We study specifically a magnetically charged black 6-brane, but show how the instability is generic, and that charge does not in general stabilise black strings and p-branes.
We study a class of topological black hole solutions in RSII braneworld scenario in the presence of a localized Maxwell field on the brane. Such a black hole can carry two types of charge, one arising from the extra dimension, the tidal charge, and the other one from a localized gauge field confined to the brane. We find that the localized charge on the brane modifies the bulk geometry and in particular the bulk Weyl tensor. The bulk geometry does not depend on different topologies of the horizons. We present the temperature and entropy expressions associated with the event horizon of the bran…
In this letter we discuss charges of D-branes on the group manifold SO(3). Our discussion will be based on a conformal field theory analysis of boundary states in a Z_2-orbifold of SU(2). This orbifold differs from the one recently discussed by Gaberdiel and Gannon in its action on the fermions and leads to a drastically different charge group. We shall consider maximally symmetric branes as well as branes with less symmetry, and find perfect agreement with a recent computation of the corresponding K-theory groups.
The flux singularity that arise when branes are put in an oppositely charged background is a wildly discussed issue and in this paper the problem is investigated further. New AdS world volume (anti-)M2-brane solutions are constructed by placing the brane in a background where the charge dissolved in the flux is opposite that of the brane. A topological obstruction is derived to show how the singularity develops during localisation of this solution and any similarly constructed solution. Furthermore the singularity is shown not to be possible to hide behind a horizon, which would have given cre…
The charges of the exceptionally twisted (D4 with triality and E6 with charge conjugation) D-branes of WZW models are determined from the microscopic/CFT point of view. The branes are labeled by twisted representations of the affine algebra, and their charge is determined to be the ground state multiplicity of the twisted representation. It is explicitly shown using Lie theory that the charge groups of these twisted branes are the same as those of the untwisted ones, confirming the macroscopic K-theoretic calculation. A key ingredient in our proof is that, surprisingly, the G2 and F4 Weyl dime…
We study the central charges of the supersymmetry algebra of branes in backgrounds corresponding to wrapped M5-branes. In the case of M5-branes wrapping a holomorphic 2-cycle in two complex-dimensional space, we find this allows for a supersymmetric M5-brane probe which is related to the M2-brane probe which describes the BPS spectra of the corresponding N=2 worldvolume gauge theory. For the case of M5-branes wrapping a holomorphic 2-cycle in three complex-dimensional space, we find that the central charges allow for a supersymmetric M5-brane probe wrapping a Cayley calibrated 4-cycle, which h…
We discuss some physical issues related to the K-theoretic classification of D-brane charges, putting an emphasis on the role of D-brane instantons. The relation to D-instantons provides a physical interpretation to the mathematical algorithm for computing K-theory known as the ``Atiyah-Hirzebruch spectral sequence.'' Conjecturally, a formulation in terms of D-instantons leads to a computationally useful formulation of K-homology in general. As an application and illustration of this viewpoint we discuss some issues connected with D-brane charges associated with branes in WZW models. We discus…
The RR Page charges for the D(2p+1)-branes with B-field in type IIB supergravity are constructed consistently from brane source currents. The resulting Page charges are B-independent in the nontrivial and intricate way. It is found that in topologically trivial B-field the Page charge is conserved, but in the topologically nontrivial B-field it is no longer to be conserved, instead there is a jump between two Page charges defined in each patch, and we interpret this jump as Hanany-Witten effect.
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 explore superconducting instabilities of black branes in SO(6) gauged supergravity at finite temperature and finite R-charge densities. We compute the critical temperatures for homogeneous neutral and superconducting instabilities in a truncation of 20 scalars and 15 gauge fields as a function of the chemical potentials conjugate to the three U(1) charges in SO(6). We find that despite the imbalance provided by multiple chemical potentials there is always at least one superconducting black brane branch, emerging at a temperature where the normal phase is locally thermodynamically stable. We…
We relate, in 10 and 11 dimensional supergravities, configurations of intersecting closed branes with vanishing binding energy to configurations where one of the branes opens and has its boundaries attached to the other. These boundaries are charged with respect to fields living on the closed brane. The latter hosts electric and magnetic charges stemming from dual pairs of open branes terminating on it. We show that charge conservation, gauge invariance and supersymmetry entirely determine these charges and these fields, which can be seen as Goldstone fields of broken supersymmetry. Open brane…
By exploiting the correspondence between the Cardy boundary state in SU(2) group manifold and the BPS D3-brane configuration in the full asymptotically flat geometry of NS5-branes, we show that the Hanany-Witten effect in 10D background is encoded in the Cardy boundary states. The two RR Page D0 charges of the $n$-th spherical D2-brane due to the contraction to $e$ or ($-e$) is interpreted, and attributed to the Hanany-Witten effect.
We focus on black branes and toroidal black holes in N=2 gauged supergravities that asymptote to AdS_4, and derive formulas for the mass and central charge densities. We derive the corresponding BPS bound from the superalgebra of the asymptotic vacuum and illustrate our procedure with explicit examples of genuine black brane solutions with non-trivial scalars.
We construct supergravity solutions for D-branes in nontrivial flux backgrounds. We revisit the issue of charge quantization in this framework, and show that in these backgrounds, charge need not be quantized. We also show in a particular example that the semiclassical description of branes produces integral charges.
We show that a D-brane in a group manifold given by a (twisted) conjugacy class is characterised by a gauge invariant two-form field determined in terms of the matrix of gluing conditions. Using a quantisation argument based on the path integral one obtains the known quantisation condition for the corresponding D-branes. We find no evidence for the existence of a quantised U(1) gauge field flux. We propose an expression for the D0 charge of such D-branes.
By using the boundary derivative expansion formalism of fluid/gravity correspondence, we study the chiral vortical effect from the compactified D4-branes with smeared D0-brane charge. This background corresponds to a strongly coupled, nonconformal relativistic fluid with a conserved vector current. The presence of the chiral vortical effect is induced by the addition of a Chern-Simons term in the bulk action. Except that the non-dissipative anomalous viscous coefficient and the sound speed rely only on the chemical potential, most of the other thermal and hydrodynamical quantities of the first…
We construct Gepner models in terms of coset conformal field theories and compute their twisted equivariant K-theories. These classify the D-brane charges on the associated geometric backgrounds and therefore agree with the topological K-theories. We show this agreement for various cases, in particular the Fermat quintic.
We consider a theory in which supersymmetry is partially spontaneously broken and show that the dynamical fields in the same supersymmetric multiplet as the Goldstino are Goldstone bosons whose corresponding generators are central charges in the underlying supersymmetry algebra. We illustrate how this works for four dimensional Born-Infeld theory and five brane of M theory. We conjecture, with supporting arguments, that the dynamics of the branes of M theory can be extended so as to possess an E_{11} symmetry.
In the BRST-BFV scheme for noncommutative D-branes with constant NS $B$-field, introducing ghost degrees of freedom we construct the gauge fixed Hamiltonian and corresponding effective Lagrangian invariant under nilpotent BRST charge. It is also shown that the presence of auxiliary variables introduced via the improved Dirac formalism plays a crucial role in the construction of the BRST invariant Lagrangian.
Polchinski's recent construction of Dirichlet-branes of R-R charges, together with Witten's mechanism for forming bound states of both NS-NS charges and R-R charges, provides a rigorous method to treat these dy-branes. We construct the massless sector of boundary states of D-branes, as well as of dy-strings of charge $(p,1)$. As a consequence, the string tension formula predicted by duality in the type IIB theory is obtained.
The production of string charge during a crossing of certain oriented D-branes is studied. We compute the string charge in the system of a probe D2-brane and a background D6-brane by use of the equations of motion in the ten-dimensions. We confirm the creation of string charge as inflow from the background D6-brane.
We present a class of two-charged intersecting brane solutions of the D=11 supergravity, which contain the M2-brane, M5-brane, Kaluza-Klein monopole or Brinkmann wave as their building blocks. These solutions share the common feature that one charge is smeared out or uniform over all spatial directions occupied by the branes or waves, while the other charge is localized in them.
We propose a method to investigate the conservation of brane charges at the intersection of two or more branes using the Thom classes of their normal bundles. In particular we find a relation between the charge of the branes involved in the configuration and the charge of the defects on the branes due to the intersection. We also explore the applications of our method for various brane intersections in type II strings and M-theory.
A black hole solution to low energy type IIA string theory which is extremal, non-supersymmetric, and carries 0- and 6-brane charge is presented. For large values of the charges it is metastable and a corresponding D-brane picture can be found. The mass and statistical entropy of the two descriptions agree at a correspondence point up to factors of order one, providing more evidence that the correspondence principle for black holes and strings of Horowitz and Polchinski may be extended to include black holes with more than one Ramond-Ramond charge.
We construct new D-brane bound states using charged macroscopic type IIB string solutions.A generic bound state solution, when dimensionally reduced, carries multiple gauge charges. Starting with D=9 charged macroscopic strings, we obtain solutions in D=10, which are interpreted as carrying (F, D0, D2) charges as well as nonzero momenta. The masses and charges are also explicitly shown to satisfy the non-threshold bound of 1/2 BPS objects. Our solutions reduce to the known D-brane bound state solutions with appropriate restrictions in the parameter space. We further generalize the results to (…
We construct families of supersymmetric AdS$_3\times Y_7$ and AdS$_3\times Y_8$ solutions to type IIB string theory and M-theory, respectively. Here $Y_7$ is an $S^5$ fibration over $Σ$, while $Y_8$ is an $S^4$ fibration over $Σ_g\times Σ$, where $Σ_g$ is a Riemann surface of genus $g>1$ and $Σ$ is a two-dimensional orbifold known as a spindle. We interpret the solutions as near-horizon limits of $N$ D3-branes wrapped on $Σ$ and $N$ M5-branes wrapped on $Σ_g\times Σ$, respectively. These are holographically dual to $d=2$, $(0,2)$ SCFTs, and we show that the central charge and superconformal R-…
We consider the inclusion of brane charges in AdS_5 superalgebras that contain the maximal central extension of the super-Poincaré algebra on the boundary of AdS_5. For theories with N supersymmetries on the boundary, the maximal extension is OSp(1/8N,R), which contains the group $Sp(8N,R)\supset U(2N,2N) \supset SU(2,2)\times U(N)$ as extension of the conformal group. An ``intermediate'' extension to U(2N,2N/1) is also discussed, as well as the inclusion of brane charges in AdS_7 and AdS_4 superalgebras. BPS conditions in the presence of brane charges are studied in some details.
We investigate the space of BPS states in type IIA string theory on a T$^6$ wrapped by one D6 brane and three D2 branes wrapping three disjoint 2-tori. This system of branes has 12 ground states. We show that these 12 states are all recovered as Coulomb branch BPS multicenter bound states, in which each center preserves 16 supercharges. Moreover, we show that these multicenter solutions can only exist with zero angular momentum, supporting the conjecture that all black hole microstates have zero angular momentum. For large charges, they might describe "near-horizon limit" of fuzzballs.
We propose a simple form for the superalgebra of M2 and M5-brane probes in arbitrary supersymmetric backgrounds of 11D supergravity, extending previous results in the literature. In particular, we identify the topological charges in the algebras and find BPS bounds for the energies. The charges are given by the integral over a brane's spatial worldvolume of a certain closed form built out of the Killing spinors and background fields. The existence of such closed forms for arbitrary supersymmetric backgrounds generalises the existence of calibration forms for special holonomy manifolds.
We study the properties of half-supersymmetric branes in string theory with 32 supercharges from a purely group-theoretical point of view using the U-duality symmetry of maximal supergravity and the R-symmetry of the corresponding supersymmetry algebra. In particular, we show that half-supersymmetric branes are always associated to the longest weights of the U-duality representation of the potentials coupling to them. We compare the features of branes with three or more transverse directions (that we call "standard" branes) to those with two or less transverse directions (that we denominate "n…
We study electrically charged asymptotically flat black brane solutions whose world-volume fields are slowly varying with the coordinates. Using familiar techniques, we compute the transport coefficients of the fluid dynamic derivative expansion to first order. We show how the shear and bulk viscosities are modified in the presence of electric charge and we compute the charge diffusion constant which is not present for the neutral black p-brane. We compute the first order dispersion relations of the effective fluid. For small values of the charge the speed of sound is found to be imaginary and…
We discuss a 4-dimensional nonsupersymmetric black hole solution to low energy type IIA string theory which carries D0- and D6-brane charges. For equal charges this solution reduces to the one discussed recently by Sheinblatt. We present a new parametrization of the solution in terms of four numbers which reveals the underlying brane and antibrane structure of the black hole arbitrarily far from extremality. In this parametrization, the entropy of the general nonextremal black hole takes on a simple U-duality invariant form. A Yang-Mills solution for the brane configuration corresponding to th…
The D-brane counting of black hole entropy is commonly understood in terms of excitations carrying fractional charges living on long, multiply-wound branes (e.g. open strings with fractional Kaluza-Klein momentum). This paper addresses why the branes become multiply wound. Since multiply wound branes are T-dual to branes evenly spaced around the compact dimension, this tendency for branes to become multiply wound can be seen as an effective repulsion between branes in the T-dual picture. We also discuss how the fractional charges on multiply wound branes conspire to always form configurations …
The problem of finding supersymmetric brane configurations in the near-horizon attractor geometry of a Calabi-Yau black hole with magnetic-electric charges (p^I,q_I) is considered. Half-BPS configurations, which are static for some choice of global AdS2 coordinate, are found for wrapped brane configurations with essentially any four-dimensional charges (u^I,v_I). Half-BPS multibrane configurations can also be found for any collection of wrapped branes provided they all have the same sign for the symplectic inner product p^Iv_I-u^Iq_I of their charges with the black hole charges. This contrasts…
We analyze exactly the simplest minimal superstring theory, using its dual matrix model. Its target space is one dimensional (the Liouville direction), and the background fields include a linear dilaton, a possible tachyon condensate, and RR flux. The theory has both charged and neutral branes, and these exhibit new and surprising phenomena. The smooth moduli space of charged branes has different weakly coupled boundaries in which the branes have different RR charges. This new duality between branes of different charges shows that the semiclassical notion of localized charge is not precise in …
We propose that N M5-branes, put on R^4/Z_m with deformation parameters epsilon_{1,2}, realize two-dimensional theory with SU(m)_N symmetry and m-th para-W_N symmetry. This includes the standard W_N symmetry for m=1 and super-Viraroro symmetry for m=N=2. We provide a small check of this proposal by calculating the central charge of the 2d theory from the anomaly polynomial of the 6d theory.
In this paper, based on the principles of gauge/gravity duality and considering the so called \textit{hydrodynamic} limit we compute various charge transport properties for a class of strongly coupled non relativistic CFTs corresponding to $ z=2 $ fixed point whose dual gravitational counter part could be realized as the consistent truncation of certain non relativistic $ Dp $ branes in the non extremal limit. From our analysis we note that unlike the case for the AdS black branes, the charge diffusion constant in the non relativistic background scales differently with the temperature. This sh…
The maximally symmetric D-branes of string theory on the non-simply connected Lie group SU(n)/Z_d are analysed using conformal field theory methods, and their charges are determined. Unlike the well understood case for simply connected groups, the charge equations do not determine the charges uniquely, and the charge group associated to these D-branes is therefore in general not cyclic. The precise structure of the charge group depends on some number theoretic properties of n, d, and the level of the underlying affine algebra k. The examples of SO(3)=SU(2)/Z_2 and SU(3)/Z_3 are worked out in d…
We consider general properties of central charges of zero branes and associated duality invariants, in view of their double role, on the bulk and on the world volume (quantum-mechanical) theory. A detailed study of the BPS condition for the mass spectrum arising from toroidal compactifications is given for 1/2, 1/4 and 1/8 BPS states in any dimensions. As a byproduct, we retreive the U-duality invariant conditions on the charge (zero mode) spectrum and the orbit classification of BPS states preserving different fractions of supersymmetry. The BPS condition for 0-branes in theories with 16 supe…
Brane bound states, deformations and OM
本文研究了多项矢量变形对膜背景的影响，发现不同矢量变形会引入不同类型的膜电荷，并探讨了这些结果在NRCS和OM理论中的意义。
We construct gauge-invariant and U-duality covariant expressions for Wess-Zumino terms corresponding to general Dp-branes (for any p<D) in arbitrary 2<D<11 dimensions. A distinguishing feature of these Wess-Zumino terms is that they contain twice as many scalars as the 10-D compactified dimensions, in line with doubled geometry. We find that for D<10 the charges of the higher-dimensional branes can all be expressed as products of the 0-brane charges, which include the D0-brane and the NS-NS 0-brane charges. We give the general expressions for these charges and show how they determine the non-t…
We compute the boundary state corresponding to a fractional D$p$-brane with transverse motion and internal background fields: Kalb-Ramond and a $U(1)$ gauge field. The spacetime has the orbifold structure $\mathbb{R}^{1,5} \times\mathbb{C}^{2}/\mathbb{Z}_{2}$. The calculations are in the superstring theory. Using this boundary state we shall obtain the interaction amplitude between two parallel moving fractional D$p$-branes. We shall extract behavior of the interaction amplitude for large distances of the branes.
D-branes that appear to generate all the K-theory charges of string theory on SU(n) are constructed, and their charges are determined.
D-brane tension as central charge
利用哈密顿方法，从开弦场论推导D0-膜质量作为26维庞加莱代数自发破缺的中心荷。
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