Brane-antibrane Pairs Research Articles

Cosmology from confinement?

We describe a class of holographic models that may describe the physics of certain four-dimensional big-bang/big-crunch cosmologies. The construction involves a pair of 3D Euclidean holographic CFTs each on a homogeneous and isotropic space M coupled at either end of an interval ℐ to a Euclidean 4D CFT on M × ℐ with many fewer local degrees of freedom. We argue that in some cases, when the size of M is much greater than the length of ℐ, the theory flows to a confining three-dimensional field theory on M in the infrared, and this is reflected in the dual description by the asymptotically AdS spacetimes dual to the two 3D CFTs joining up in the IR to give a Euclidean wormhole. The Euclidean construction can be reinterpreted as generating a state of the Lorentzian 4D CFT on M × time whose dual includes the physics of a big-bang/big-crunch cosmology. When M is ℝ3, we can alternatively analytically continue one of the ℝ3 directions to get an eternally traversable four-dimensional planar wormhole. We suggest explicit microscopic examples where the 4D CFT is mathcal{N} = 4 SYM theory and the 3D CFTs are superconformal field theories with opposite orientation. In this case, the two geometries dual to the pair of 3D SCFTs can be understood as a geometrical version of a brane-antibrane pair, and the tendency of the geometries to connect up is related to the standard instability of brane-antibrane systems.

Topological insulators and the QCD vacuum: The theta parameter as a Berry phase

There is considerable evidence, based on large ${N}_{c}$ chiral dynamics, holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by discrete quasivacua separated by domain walls across which the local value of the topological $\ensuremath{\theta}$ parameter jumps by $\ifmmode\pm\else\textpm\fi{}2\ensuremath{\pi}$. This scenario is realized in a 2D U(1) gauge theory, the $C{P}^{N\ensuremath{-}1}$ sigma model, where a pointlike charge is a domain wall, and $\ensuremath{\theta}$ describes the background electric flux and the polarization of charged pairs in the vacuum. The transition between discrete $\ensuremath{\theta}$ vacua occurs via the transport of integer units of charge between the two spatial boundaries of the domain. We show that this screening process, and the role of $\ensuremath{\theta}$ as an order parameter describing electric polarization, are naturally formulated in terms of Bloch wave eigenstates of the Dirac Hamiltonian in the background gauge field. This formulation is similar to the Berry phase description of electric polarization and quantized charge transport in topological insulators. The Bloch waves are quasiperiodic superpositions of localized Dirac zero modes and the charge transport takes place coherently via topological charge-induced spectral flow. The adiabatic spectral parameter becomes the Bloch wave momentum, which defines a Berry connection around the Brillouin zone of the zero mode band. It describes the local polarization of vacuum pairs, analogous to its role in topological insulator theory. In 4D Yang-Mills theory, the $\ensuremath{\theta}$ domain walls are $2+1$-dimensional Chern-Simons membranes, and the $\ensuremath{\theta}$ parameter describes the local polarization of brane-antibrane pairs. The topological description of polarization in 2D U(1) gauge theory generalizes to membrane polarization in 4D QCD by exploiting a relationship between the Berry connection and the gauge cohomology structure encoded in the descent equations of 4D Yang-Mills theory.

Topological insulators and the QCD vacuum: the theta parameter as a Berry phase

There is considerable evidence, based on large $N_c$ chiral dynamics, holographic QCD, and Monte Carlo studies, that the QCD vacuum is permeated by discrete quasivacua separated by domain walls across which the local value of the topological $\theta$ parameter jumps by $\pm2\pi$. In the 2-dimensional $CP^{N-1}$ sigma model, a pointlike charge is a domain wall, and $\theta$ describes the background electric flux and the polarization of charged pairs in the vacuum. We show that the screening process, and the role of $\theta$ as an order parameter describing electric polarization, are naturally formulated in terms of Bloch wave eigenstates of the Dirac Hamiltonian in the background gauge field. This formulation is similar to the Berry phase description of electric polarization and quantized charge transport in topological insulators. The Bloch waves are quasiperiodic superpositions of localized Dirac zero modes. They define a Berry connection around the Brillouin zone of the zero mode band which describes the local polarization of vacuum pairs, analogous to its role in topological insulator theory. In 4D Yang-Mills theory, the $\theta$ domain walls are 2+1-dimensional Chern-Simons membranes. The interpretation of the $\theta$ parameter as a Berry phase describing the local polarization of brane-antibrane pairs follows from the descent equations of 4D Yang-Mills theory.

Tachyon Condensation and Brane Annihilation in Bose-Einstein Condensates: Spontaneous Symmetry Breaking in Restricted Lower-Dimensional Subspace

In brane cosmology, the Big Bang is hypothesized to occur by the annihilation of the brane–anti-brane pair in a collision, where the branes are three-dimensional objects in a higher-dimensional Universe. Spontaneous symmetry breaking accompanied by the formation of lower-dimensional topological defects, e.g. cosmic strings, is triggered by the so-called ‘tachyon condensation’, where the existence of tachyons is attributable to the instability of the brane–anti-brane system. Here, we discuss the closest analogue of the tachyon condensation in atomic Bose–Einstein condensates. We consider annihilation of domain walls, namely branes, in strongly segregated two-component condensates, where one component is sandwiched by two domains of the other component. In this system, the process of the brane annihilation can be projected effectively as ferromagnetic ordering dynamics onto a two-dimensional space. Based on this correspondence, three-dimensional formation of vortices from a domain-wall annihilation is considered to be a kink formation due to spontaneous symmetry breaking in the two-dimensional space. We also discuss a mechanism to create a ‘vorton’ when the sandwiched component has a vortex string bridged between the branes. We hope that this study motivates experimental researches to realize this exotic phenomenon of spontaneous symmetry breaking in superfluid systems.

Brane-antibrane backreaction in axion monodromy inflation

We calculate the interaction potential between D5 and D̄5 braneswrapping distant but homologous 2-cycles. The interaction potential is logarithmic in the separationradius and does not decouple at infinity. We show that logarithmic backreaction is generic for 5-branes wrapping distant but homologous 2-cycles, and we argue that this destabilises models of axion monodromy inflation involvingNS5 brane-antibrane pairs in separate warped throats towards an uncontrolled region.

On higher rank coisotropic [formula omitted]-branes

This article is devoted to a world sheet analysis of A -type D -branes in N = ( 2 , 2 ) supersymmetric non-linear sigma models. In addition to the familiar Lagrangian submanifolds with flat connection we reproduce the rank one A -branes of Kapustin and Orlov, which are supported on coisotropic submanifolds. The main focus is however on gauge fields of higher rank and on tachyon profiles on brane–antibrane pairs. This will lead to the notion of a complex of coisotropic A -branes. A particular role is played by the noncommutative geometry on the brane world volume. It ensures that brane–antibrane pairs localize again on coisotropic submanifolds.

Tachyon condensation on separated brane-antibrane system

We study the effect of tachyon condensation on a brane antibrane pair in superstring theory separated in the transverse direction. The static properties of the tachyon potential analyzed using level truncated string field theory reproduces the desired property that the dependence of the minimum value of the potential on the initial distance of separation between the branes decreases as we include higher level terms. The rolling tachyon solution constructed using the conformal field theory methods shows that if the initial separation between the branes is less than a critical distance then the solution is described by an exactly marginal deformation of the original conformal field theory where the correlation functions of the deformed theory are determined completely in terms of the correlation functions of the undeformed theory without any need to regularize the theory. Using this we give an expression for the pressure on the brane-antibrane system as a power series expansion in exp(Cx0) for an appropriate constant C.

Perturbations and moduli space dynamics of tachyon kinks

The dynamic process of unstable D-branes decaying into stable ones with one dimension lower can be described by a tachyon field with a Dirac-Born-Infeld effective action. In this paper we investigate the fluctuation modes of the tachyon field around a two-parameter family of static solutions representing an array of brane-antibrane pairs. Besides a pair of zero modes associated with the parameters of the solution, and instabilities associated with annihilation of the brane-antibrane pairs, we find states corresponding to excitations of the tachyon field around the brane and in the bulk. In the limit that the brane thickness tends to zero, the support of the eigenmodes is limited to the brane, consistent with the idea that propagating tachyon modes drop out of the spectrum as the tachyon field approaches its ground state. The zero modes, and other low-lying excited states, show a fourfold degeneracy in this limit, which can be identified with some of the massless superstring modes in the brane-antibrane system. Finally, we also discuss the slow motion of the solution corresponding to the decay process in the moduli space, finding a trajectory which oscillates periodically between the unstable D-brane and the brane-antibrane pairs of one dimension lower.

Relic topological defects from brane annihilation simulated in superfluid 3He

Although it is widely accepted that to resolve the ‘horizon’ problem the early Universe must have undergone a sudden expansion (cosmic inflation), what mechanism drove this process is less clear. In the braneworld scenario, it is suggested that inflationary epochs may have been initiated and terminated by brane collisions and annihilations1,2,3. Branes are objects of lower dimensionality embedded in a higher-dimensional matrix. For example, we may live on a three-dimensional brane embedded in a four-dimensional matrix. However, such structures are so far removed from everyday reality that bringing physical insight to bear is difficult. Here we report laboratory experiments where we simulate brane annihilation using the closest brane analogue to which we have access, the coherent phase boundary between the two phases of superfluid 3He. When two branes collide or annihilate, topological defects may be created, whose influence may still be detectable today. By creating a brane–antibrane pair in superfluid 3He and subsequently annihilating it, we can detect that defects are indeed created in the superfluid texture (the superfluid analogue of spacetime), thus confirming that the concept of defect formation after brane annihilation in the early Universe can be reproduced in analogous systems in the laboratory.

Metastable string vacua

We argue that tachyon-free type I string vacua with supersymmetry breaking in the open sector at the string scale can be interpreted, via S- and T-duality arguments, as metastable vacua of the supersymmetric type I superstring. The dynamics of the process can be partly captured via nucleation of brane–anti-brane pairs out of the non-supersymmetric vacuum and subsequent tachyon condensation.

On tadpoles and vacuum redefinitions in String Theory

Tadpoles accompany, in one form or another, all attempts to realize supersymmetry breaking in String Theory, making the present constructions at best incomplete. Whereas these tadpoles are typically large, a closer look at the problem from a perturbative viewpoint has the potential of illuminating at least some of its qualitative features in String Theory. A possible scheme to this effect was proposed long ago by Fischler and Susskind, but incorporating background redefinitions in string amplitudes in a systematic fashion has long proved very difficult. In the first part of this paper, drawing from field theory examples, we thus begin to explore what one can learn by working perturbatively in a “wrong” vacuum. While unnatural in Field Theory, this procedure presents evident advantages in String Theory, whose definition in curved backgrounds is mostly beyond reach at the present time. At the field theory level, we also identify and characterize some special choices of vacua where tadpole resummations terminate after a few contributions. In the second part we present a notable example where vacuum redefinitions can be dealt with to some extent at the full string level, providing some evidence for a new link between IIB and 0B orientifolds. We finally show that NS–NS tadpoles do not manifest themselves to lowest order in certain classes of string constructions with broken supersymmetry and parallel branes, including brane–antibrane pairs and brane supersymmetry breaking models, that therefore have UV-finite threshold corrections at one loop.

Finite Temperature Systems of Brane-Antibrane Pairs and Non-BPS D-Branes

We investigate the thermodynamic properties of D-brane-anti-D-brane pairs and non-BPS D-branes on the basis of boundary string field theory. We calculate the finite temperature effective potential of N D-brane-anti-D-brane pairs in a non-compact background and in a toroidal background. In the non-compact background case, a phase transition occurs slightly below the Hagedorn temperature, and the D9-anti-D9 pairs become stable. Moreover, the total energy at the critical temperature is a decreasing function of N as long as the 't Hooft coupling is very small. This leads to the conclusion that a large number N of D9-anti-D9 pairs are created simultaneously near the Hagedorn temperature. In the toroidal background case (M_{1,9-D} * T_{D}), a phase transition occurs only if the Dp-anti-Dp pair is extended in all the non-compact directions, as long as the 't Hooft coupling is very small. The total energy at the critical temperature also decreases as N increases. We also calculate the finite temperature effective potential of non-BPS D-branes, and we obtain similar results. Then, we consider the thermodynamic balance between open strings on these branes and closed strings in the bulk in the ideal gas approximation, and conclude that the total energy is dominated by the open strings.

From branes to branes

We use the ‘branes within branes’ approach to study the appearance of stable ( p−2)-branes and unstable ( p−1)-branes in type II string theory from p-brane– p-antibrane pairs. Our goal is to describe the emergence of these lower-dimensional branes from brane–antibrane pairs in string theory using a tractable gauge theory language. This is achieved by suspending the original p-brane– p-antibrane pair between two ( p+2)-branes, and describing its dynamics in terms of the worldvolume gauge theory on the spectator ( p+2)-branes. Instantons, monopoles, sphalerons and their higher-dimensional generalizations in this worldvolume gauge theory correspond to stable (BPS) and unstable (non-BPS) branes in string theory. Collisions of stable branes with corresponding antibranes and production of lower-dimensional branes in string theory are described in a straightforward way in gauge theory. Tachyonic modes on the p-brane– p-antibrane worldvolume do not appear in our analysis since we work on the worldvolume of the spectator ( p+2)-branes. Our results on brane descent relations are in agreement with Sen's tachyon condensation approach.

Time Evolution of Rolling Tachyons for a Brane-Antibrane Pair

A precise form of the time evolution of rolling tachyons corresponding to a brane-antibrane pair is investigated by solving the Hamiltonian equations of motion under the assumption that in a region far away from branes the tachyon vacuum is almost already achieved, even at the beginning of the rolling.

Dirac-Born-Infeld action on the tachyon kink and vortex

The tachyon effective field theory describing the dynamics of a non-Bogomol'nyi-Prasad-Sommerfield (BPS) D-brane in superstring theory has an infinitely thin but finite tension kink solution describing a codimension one BPS D-brane. We study the world-volume theory of massless modes on the kink, and show that the world volume action has precisely the Dirac-Born-Infeld (DBI) form without any higher derivative corrections. We generalize this to a vortex solution in the effective field theory on a brane-antibrane pair. As in the case of the kink, the vortex is infinitely thin, has finite energy density, and the world-volume action on the vortex is again given exactly by the DBI action on a BPS D-brane. We also discuss the coupling of fermions and restoration of supersymmetry and $\ensuremath{\kappa}$ symmetry on the world volume of the kink. The absence of higher derivative corrections to the DBI action on the soliton implies that all such corrections are related to higher derivative corrections to the original effective action on the world volume of a non-BPS D-brane or brane-antibrane pair.

Brane–anti-brane systems interaction under tachyon condensation

The interaction between a parallel brane–anti-brane and brane–anti-brane is investigated by regarding the brane–anti-brane pair as a kink or anti-kink type tachyon condensed state. As the kink-type tachyon condensed state is known as a non-BPS brane we expand the Lagrangian of tachyon effective field theory to the quadratic order in the off-diagonal fluctuation and then use the zeta-function regularization and Schwinger perturbative formula to evaluate the interaction within a kink–kink or a kink–anti-kink. The results show that while the kink and kink has repulsive force the kink and anti-kink has attractive force and may annihilate by each other. We, therefore, evaluate the free energy at finite temperature and determine the critical temperature above which the stable state of kink–anti-kink system may be found.

Brane-Antibrane Systems at Finite Temperature and Phase Transition near the Hagedorn Temperature

In order to study the thermodynamic properties of brane-antibrane systems, we compute the finite temperature effective potential of tachyon T in this system on the basis of boundary string field theory. At low temperature, the minimum of the potential shifts towards T=0 as the temperature increases. In the D9-antiD9 case, the sign of the coefficient of |T|^2 term of the potential changes slightly below the Hagedorn temperature. This means that a phase transition occurs near the Hagedorn temperature. On the other hand, the coefficient is kept negative in the Dp-antiDp case with p <= 8, and thus a phase transition does not occur. This leads us to the conclusion that only a D9-antiD9 pair and no other (lower dimensional) brane-antibrane pairs are created near the Hagedorn temperature. We also discuss a phase transition in NS9B-antiNS9B case as a model of the Hagedorn transition of closed strings.

Dynamical Decay of Brane-Antibrane and Dielectric Brane

Using D-brane effective field theories, we study dynamical decay of unstable brane systems : (i) a parallel brane-antibrane pair with separation l and (ii) a dielectric brane. In particular we give explicitly the decay width of these unstable systems, and describe how the decay proceeds after the tunnel effect. The decay (i) is analysed by the use of a tachyon effective action on the Dp-Dpbar. A pair annihilation starts by nucleation of a bubble of a tachyon domain wall which represents a throat connecting these branes, and the tunneling decay width is found to be proportional to exp(-l^{p+1} T_{Dp}). We study also the decay leaving topological defects corresponding to lower-dimensional branes, which may be relevant for recent inflationary braneworld scenario. As for the decay (ii), first we observe that Dp-branes generically ``curl up'' in a nontrivial RR field strength. Using this viewpoint, we compute the decay width of the dielectric D2-branes by constructing relevant Euclidean bounce solutions in the shape of a funnel. We also give new solutions in doughnut shape which are involved with nucleation of dielectric branes from nothing.

From p-branes to fluxbranes and back

In this note we study aspects of the interplay between fluxbranes and p-branes. We describe how a fluxbrane can be physically realized as a limit of a brane-antibrane configuration, in a manner similar to the way a uniform electric field appears in between the plates of a capacitor. We also study the evolution of a fluxbrane after nucleation of p-branes. We find that Kaluza-Klein fluxbranes do relax by forming brane-antibrane pairs or spherical branes, but we also find that for fluxtubes with dilaton coupling in a different range, the field strength does not relax, instead it becomes stronger after each nucleation bounce. We speculate on a possible runaway instability of such fluxtubes an an eventual breakdown of their classical description.

Conformal boundary states for free bosons and fermions

A family of conformal boundary states for a free boson on a circle is constructed. The family contains superpositions of conventional U(1)-preserving Neumann and Dirichlet branes, but for general parameter values the boundary states are fundamental and preserve only the conformal symmetry. The relative overlaps satisfy Cardy's condition, and each boundary state obeys the factorisation constraint. It is also argued that, together with the conventional Neumann and Dirichlet branes, these boundary states already account for all fundamental conformal D-branes of the free boson theory. The results can be generalised to the situation with N=1 world-sheet supersymmetry, for which the family of boundary states interpolates between superpositions of non-BPS branes and combinations of conventional brane anti-brane pairs.