We study properties of non-BPS D(p+1)-brane in the background of k NS5-branes, with one transverse direction compactified on a circle, from the point of view of Dirac-Born-Infeld action. We present the analysis of two different embedding of non-BPS D(p+1)-brane in given background and study the classical solutions of given world-volume theory. We argue for the configuration of a non-BPS D(p+1)-brane which allows us to find solutions of the equations of motion that give unified descriptions of G and U-type branes.
We present the study of the dynamics of the geometrical tachyon field on an unstable D3-brane in the background of a bulk tachyon field of a D3-brane solution of Type-0 string theory. We find that the geometrical tachyon potential is modified by a function of the bulk tachyon and inflation occurs at weak string coupling, where the bulk tachyon condenses, near the top of the geometrical tachyon potential. We also find a late accelerating phase when the bulk tachyon asymptotes to zero and the geometrical tachyon field reaches the minimum of the potential.
We further investigate the $NS$5 ring background using the tachyon map. Mapping the radion fields to the rolling tachyon helps to explain the motion of a probe $Dp$-brane in this background. It turns out that the radion field becomes tachyonic when the brane is confined to one dimensional motion inside the ring. We find explicit solutions for the geometrical tachyon field that describe stable kink solutions which are similar to those of the open string tachyon. Interestingly in the case of the geometric tachyon, the dynamics is controlled by a cosine potential. In addition, we couple a constan…
We study the dynamics of a D3-brane moving in the background of a bulk tachyon field of a D3-brane solution of Type-0 string theory. We show that the dynamics on the probe D3-brane can be described by a geometrical tachyon field rolling down its potential which is modified by a function of the bulk tachyon and inflation occurs at weak string coupling, where the bulk tachyon condenses, near the top of the geometrical tachyon potential. We also find a late accelerating phase when the bulk tachyon asymptotes to zero which in the geometrical tachyon picture corresponds to the minimum of the geomet…
We propose an alternative formulation of tachyon inflation using the geometrical tachyon arising from the time dependent motion of a BPS $D3$-brane in the background geometry due to $k$ parallel $NS$5-branes arranged around a ring of radius $R $. Due to the fact that the mass of this geometrical tachyon field is $\sqrt{2/k} $ times smaller than the corresponding open-string tachyon mass, we find that the slow roll conditions for inflation and the number of e-foldings can be satisfied in a manner that is consistent with an effective 4-dimensional model and with a perturbative string coupling. W…
We investigate the dynamics of a pair of coincident D5 branes in the background of $k$ NS5 branes. It has been proposed by Kutasov that the system with a single probing D-brane moving radially in this background is dual to the tachyonic DBI action for a non-BPS Dp brane. We extend this proposal to the non-abelian case and find that the duality still holds provided one promotes the radial direction to a matrix valued field associated with a non-abelian geometric tachyon and a particular parametrization for the transverse scalar fields is chosen. The equations of motion of a pair of coincident D…
Using string field theory, we argue that the tachyon potential on a D-brane anti-D-brane system in type II string theory in arbitrary background has a universal form, independent of the boundary conformal field theory describing the brane. This implies that if at the minimum of the tachyon potential the total energy of the brane antibrane system vanishes in a particular background, then it vanishes in any other background. Similar result holds for the tachyon potential of the non-BPS D-branes of type II string theory, and the D-branes of bosonic string theory.
We show that a low-energy action for massless fluctuations around a tachyonic soliton background representing a codimension one D-brane coincides with the Dirac-Born-Infeld action. The scalar modes which describe transverse oscillations of the D-brane are translational collective coordinates of the soliton. The appearance of the DBI action is a universal feature independent of details of a tachyon effective action, provided it has the structure implied by the open string sigma model partition function.
A system of k Neveu-Schwarz (NS) 5-branes of type II string theory with one transverse direction compactified on a circle admits various unstable D-brane systems, - some with geometric instability arising out of being placed at a point of unstable equilibrium in space and some with the usual open string tachyonic instability but no geometric instability. We discuss the effect of NS 5-branes on the descent relations among these branes and their physical interpretation in the T-dual ALF spaces. We argue that if the tachyon potential controlling these descent relations obeys certain conditions, t…
We study the motion of a BPS D3-brane in the NS5-brane ring background. The radion field becomes tachyonic in this geometrical set up. We investigate the potential of this geometrical tachyon in the cosmological scenario for inflation as well as dark energy. We evaluate the spectra of scalar and tensor perturbations generated during tachyon inflation and show that this model is compatible with recent observations of Cosmic Microwave Background (CMB) due to an extra freedom of the number of NS5-branes. It is not possible to explain the origin of both inflation and dark energy by using a single …
We develop an efficient recursive method to evaluate the tachyon potential using the relevant universal subalgebra of the open string star algebra. This method, using off-shell versions of Virasoro Ward identities, avoids explicit computation of conformal transformations of operators and does not require a choice of background. We illustrate the procedure with a pedagogic computation of the level six tachyon potential in an arbitrary gauge, and the evaluation of a few simple star products. We give a background independent construction of the so-called identity of the star algebra, and show how…
In a recent paper (hep-th/0703157), Sen studied unstable D-branes in NS5-branes backgrounds and argued that in the strong curvature regime the universal open string tachyon (on D-branes of the wrong dimensionality) and the geometric tachyon (on D-branes that are BPS in flat space but not in this background) may become equivalent. We study in this note an example of a non-BPS suspended D-brane vs. a BPS D-brane at equal distance between two fivebranes. We use boundary worldsheet CFT methods to show that these two unstable branes are identical.
In this short note we perform canonical analysis of geometrical action for Dp-brane. We also discuss tachyon condensation in case of the geometrical action for unstable D(p+1)-brane.
We investigate a non-perturbative vacuum in open string field theory expanded around the analytic classical solution which has been found in the universal Fock space generated by matter Virasoro generators and ghost oscillators. We carry out level-truncation analyses up to level (6,18) in the theory around one-parameter families of the solution. We observe that the value of the vacuum energy cancels the D-brane tension as the approximation level is increased, but this non-perturbative vacuum disappears at the boundary of the parameter space. These results provide strong evidence for the conjec…
We consider tachyonic string-field fluctuations about a Dp-brane background in the geometrical (CFT) formulation of Vacuum String Field Theory. We then extend this analysis to the case of a background B-field. We find that the standard results for D-brane tension are reproduced in both cases.
We investigate de Sitter solutions of $\mathcal{N}=1$ supergravity with an F-term scalar potential near a no-scale Minkowski point, as they may in particular arise from flux compactifications in string theory. We show that a large class of such solutions has a universal tachyon with $η\le -\frac{4}{3}$ at positive vacuum energies, thus forbidding meta-stable de Sitter vacua and slow-roll inflation. The tachyon aligns with the sgoldstino in the Minkowski limit, whereas the sgoldstino itself is generically stable in the de Sitter vacuum due to mass mixing effects. We specify necessary conditions…
We use geometrical conformal field theory methods to investigate tachyon fluctuations about the butterfly projector state in Vacuum String Field Theory. We find that the on-shell condition for the tachyon field is equivalent to the requirement that the quadratic term in the string-field action vanish on shell. This further motivates the interpretation of the butterfly state as a D-brane. We begin a calculation of the tension of the butterfly, and conjecture that this will match the case of the sliver and further strengthen this interpretation.
We investigate models in which inflation is driven by a single geometrical tachyon. We assume that the D-brane as a probe brane in the background of NS5-branes has non-zero angular momentum which is shown to play similar role as the number of the scalar fields of the assisted inflation. We demonstrate that the angular momentum corrected effective potential allows to account for the observational constraint on COBE normalization, spectral index $n_S$ and the tensor to scalar ratio of perturbations consistent with WMAP seven years data.
We discuss what information can be safely extracted from background independent off-shell string theory. The major obstacle in doing so is that renormalization conditions of the underlying world-sheet theories are not exactly known. To get some insight, we first consider the tachyon and gauge field backgrounds and carry out computations in different renormalization schemes for both, bosonic string and superstring. Next, we use a principle of universality (renormalization scheme independence) to somehow compensate the missing of the renormalization conditions and get information we are looking …
We consider string theory in maximally supersymmetric type IIB plane wave background with constant five form Ramond-Ramond flux (RR plane wave). It is argued that there exists a universal sector of string configurations independent of the null coordinate $x^-$ such that the space-time action evaluated at such a configuration is same in the RR plane wave and flat background. By naturally assuming its validity for the open strings we further argue that the D-branes extending along $x^{\pm}$ are universal in these two backgrounds. Moreover, a universal D-brane which is BPS in flat space must be t…
We propose that under certain conditions the universal open string tachyon can drive topological inflation in moduli stabilised frameworks. Namely, the presence of electric field in the world volume of the D-brane can slow down its decay leading to a phenomenological model of inflation. The conditions for inflation to take place are difficult to satisfy in the standard warped deformed conifold but easier to realise in other geometries.
We consider the geometrical engineering constructions for the N = 1 SQCD vacua recently proposed by Giveon and Kutasov. After one T-duality, the geometries with wrapped D5 branes become N = 1 brane configurations with NS branes and D4 branes. The field theories encoded by the geometries contain extra massive adjoint fields for the flavor group. After performing a flop, the geometries contain branes, antibranes and branes wrapped on non-holomorphic cycles. The various tachyon condensations between pairs of wrapped D5 branes and anti D5 branes together with deformations of the cycles give rise t…
Unstable, non-BPS D-branes in weakly coupled ten dimensional string theory have many mysterious properties. Among other things, it is not clear what sets their tension, what is their relation to the better understood BPS D-branes, and why the open string tachyon on them is described by an effective Lagrangian which suggests that the tachyon corresponds to an extra spatial dimension transverse to the branes. We point out that the dynamics of D-branes in the presence of Neveu-Schwarz fivebranes on a transverse R^3 times S^1 provides a useful toy model for studying these issues. From the point of…
The D0/D4 system with a Neveu-Schwarz B-field in the spatial directions of the D4-brane has a tachyon in the spectrum of the (0,4) strings. The tachyon signals the instability of the system to form a bound state of the D0-brane with the D4-brane. We use the Wess-Zumino-Witten like open superstring field theory formulated by Berkovits to study the tachyon potential for this system. The tachyon potential lies outside the universality class of the D-brane anti-D-brane system. It is a function of the B-field. We calculate the tachyon potential at the zeroth level approximation. The minimum of the …
We compute, on the disk, the non-linear tachyon $β$-function, $β^T$, of the open bosonic string theory. $β^T$ is determined both in an expansion to the third power of the field and to all orders in derivatives and in an expansion to any power of the tachyon field in the leading order in derivatives. We construct the Witten-Shatashvili (WS) space-time effective action $S$ and prove that it has a very simple universal form in terms of the renormalized tachyon field and $β^T$. The expression for $S$ is well suited to studying both processes that are far off-shell, such as tachyon condensation, an…
An outstanding problem in open bosonic string field theory is the existence of nontrivial classical solutions in its universal sector. Such solutions independent of the underlying CFT would be relevant for any background, but aside of the celebrated tachyon vacuum, no well behaved solutions have been found so far. In this work we revisit the problem using the old fashioned level truncation technique, but armed with much more sophisticated techniques and greater computer power. In particular, using the homotopy continuation method we construct all solutions at level 6 (or 5) with twist symmetry…
In open string field theory the kinetic operator mixes matter and ghost sectors, and thus the ghost structure of classical solutions is not universal. Nevertheless, we have found from numerical analysis that certain ratios of expectation values for states involving pure ghost excitations appear to be universal. We give an analytic expression for these ratios and find good evidence that they are common to all known solutions of open string field theory, including the tachyon vacuum solution, lump solutions and string fields representing marginal deformations. We also draw attention to a close c…
In a previous paper [hep-th/0012251] we proposed a simple class of actions for string field theory around the tachyon vacuum. In this paper we search for classical solutions describing D-branes of different dimensions using the ansatz that the solutions factorize into the direct product of a matter state and a universal ghost state. We find closed form expressions for the matter state describing D-branes of all dimensions. For the space filling D25-brane the state is the matter part of the zero angle wedge state, the ``sliver'', built in [hep-th/0006240]. For the other D-brane solutions the ma…
Using the properties of gauged N=4 supergravity, we show that it is possible to derive a universal thermal effective potential that describes all possible high-temperature instabilities of the known N=4 superstrings. These instabilities are due to non-perturbative dyonic modes, which become tachyonic in a region of the thermal moduli space M={s,t,u}; M is common to all non-perturbative dual-equivalent N=4 superstrings in five dimensions. We analyse the non-perturbative thermal potential and show the existence of a phase transition at high temperatures corresponding to a condensation of 5-brane…
We review here a path-integral approach to classical mechanics and explore the geometrical meaning of this construction. In particular we bring to light a universal hidden BRS invariance and its geometrical relevance for the Cartan calculus on symplectic manifolds. Together with this BRS invariance we also show the presence of a universal hidden genuine non-relativistic supersymmetry. In an attempt to understand its geometry we make this susy local following the analogous construction done for the supersymmetric quantum mechanics of Witten.
In this note $D9$- and anti-$D9$-brane annihilation in type I string theory is probed by a $D1$-brane. We consider the covariant Green-Schwarz or twistor formulation of the probe theory. We expect the theory to be $κ$-invariant after the annihilation is completed. Conditions of the $κ$-invariance of the theory impose constraints on the background tachyon field. Solutions to the constraints define tachyon values which correspond to type I $D5$-branes as remnants of the annihilation. As a byproduct we get a theory which lies in the same universality class as the non-linear $σ$-model for the Atiy…
Consistent and covariant Lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity. This bundle is explicitly constructed and its geometrical structure will be studied. By means of the local index theorem for families of Bismut and Freed the consistent gravitational anomalies are calculated. Covariant gravitational anomalies are shown to be related with secondary characteristic classes of the universal bundle and a new set of descent equations which also contains the covariant Schwinger terms is derived. The relation between consistent a…
Knowledge of all-$α'$ higher derivative corrections to leading order BPS and non-BPS brane actions would serve in future endeavor of determining the complete form of the non-abelian BPS and tachyonic effective actions. In this paper, we note that there is a universality in the all-$α'$ order corrections to BPS and non-BPS branes. We compute amplitudes between one Ramond-Ramond $C$-field vertex operator and several SYM gauge/scalar vertex operators. Specifically, we evaluate in closed form string correlators of two-point amplitudes $\cal A^{Cϕ}$, $\cal A^{CA}$, a three-point amplitude $\cal A^{…
We consider the polarization of unstable type IIB D0-branes in the presence of a background five-form field strength. This phenomenon is studied from the point of view of the leading terms in the non-abelian Born Infeld action of the unstable D0-branes. The equations have SO(4) invariant solutions describing a non-commutative 3-sphere, which becomes a classical 3-sphere in the large N limit. We discuss the interpretation of these solutions as spherical D3-branes. The tachyon plays a tantalizingly geometrical role in relating the fuzzy S^3 geometry to that of a fuzzy S^4.
Universal Non-Gaussian Signatures from Transient Instabilities
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所交叉理论科学中心）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）；Institut d’Astrophysique de Paris, Sorbonne Université, CNRS（巴黎天体物理学研究所，索邦大学，法国国家科学研究中心）；Max Planck Institute for Physics, Werner-Heisenberg-Institut（马克斯·普朗克物理研究所，维尔纳·海森堡研究所）；Max Planck-IAS-NTU Center for Particle Physics, Cosmology and Geometry（马克斯·普朗克-国际先进研究-南洋理工大学粒子物理、宇宙学与几何中心）
Casimir forces are a manifestation of the change in the zero-point energy of the vacuum caused by the insertion of boundaries. We show how the Casimir force can be efficiently computed by consideration of the vacuum fluctuations that are suppressed by the boundaries, and rederive the scalar Casimir effects for a series of the Dirichlet geometries. For the planar case a finite universal force is automatically found. Consistent with other calculations of the effect, for curved geometries divergent (non-universal) expressions are encountered. They are interpreted geometrically following Candelas …
In this work, we study the general properties of the $D$-vector field localization on $(D-d-1)$-brane with co-dimension $d$. We consider a conformally flat metric with the warp factor depending only on the transverse extra dimensions. We employ the geometrical coupling mechanism and find an analytical solution for the $U(1)$ gauge field valid for any warp factor. Using this solution we find that the only condition necessary for localization is that the bulk geometry is asymptotically AdS. Therefore, our solution has an universal validity for any warp factor and is independent of the particular…
We consider a cosmological scenario within the KKLT framework for moduli stabilization in string theory. The universal open string tachyon of decaying non-BPS D-brane configurations is proposed to drive eternal topological inflation. Flux-induced `warping' can provide the small slow-roll parameters needed for successful inflation. Constraints on the parameter space leading to sufficient number of e-folds, exit from inflation, density perturbations and stabilization of the Kahler modulus are investigated. The conditions are difficult to satisfy in Klebanov-Strassler throats but can be satisfied…
String propagation on D-dimensional curved backgrounds with Lorentzian signature is formulated as a geometrical problem of embedding surfaces. When the spatial part of the background corresponds to a general WZW model for a compact group, the classical dynamics of the physical degrees of freedom is governed by the coset conformal field theory SO(D-1)/SO(D-2), which is universal irrespective of the particular WZW model. The same holds for string propagation on D-dimensional flat space. The integration of the corresponding Gauss-Codazzi equations requires the introduction of (non-Abelian) parafe…
We study the geometrical properties of scale-invariant two-field models of inflation. In particular, we show that when the field-derivative space in the Einstein frame is maximally symmetric during inflation, the inflationary predictions can be universal and independent of the details of the theory.
The entire S-matrix elements of four, five and six point functions of D-brane-anti D-brane system are explored. To deal with symmetries of string amplitudes as well as their all order $α'$ corrections we first address a four point function of one closed string Ramond-Ramond (RR) and two real tachyons on the world volume of brane-anti brane system. We then focus on symmetries of string theory as well as universal tachyon expansion to achieve both string and effective field theory of an RR and three tachyons where the complete algebraic analysis for the whole S-matrix $<V_{C^{-1}} V_{T^{-1}} V_{…
Using a geometrical approach to the quantum Yang-Baxter equation, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ and its universal quantum $R$-matrix are explicitely constructed as functionals of the associated classical $r$-matrix. In this framework, the quantum algebra ${\cal U}_{\hbar}(sl_{2})$ is naturally imbedded in the universal envelopping algebra of the $sl_{2}$ current algebra.
We discuss how the statistical properties of the area and radius of gyration of single self-avoiding loops, and of Ising and percolation cluster boundaries, may be calculated using ideas of two-dimensional field theory. For cluster boundaries, we show that almost all loops have area $C\ln L+O(1)$, where $L$ is the size of the system, and $C$ is a calculable constant. We also compute the universal ratios $\langle A\rangle_\ell/\langle R^2\rangle_\ell$ of the area to the squared radius of gyration of loops of a given large perimeter $\ell$.
Maslov indices in periodic-orbit theory are investigated using phase space path integral. Based on the observation that the Maslov index is the multi-valued function of the monodromy matrix, we introduce a generalized monodromy matrix in the universal covering space of the symplectic group and show that this index is uniquely determined in this space. The stability of the orbit is shown to determine the parity of the index, and a formula for the index of the n-repetition of the orbit is derived.
It is known that a five-dimensional free vector field $A_{M}$ cannot be localized on Randall-Sundrum (RS)-like thick branes, namely, the thick branes embedded in asymptotic Anti-de Sitter (AdS) spacetime. In order to localize a vector field on the RS-like thick brane, an extra coupling term should be introduced. In this paper, we generalize the geometrical coupling mechanism by adding two mass terms ($αRg^{MN}A_{M}A_{N}+βR^{MN}A_{M}A_{N}$) into the action. We decompose the fundamental vector field $A_{M}$ into three parts: transverse vector part $\hat{A}_μ$, scalar parts $ϕ$ and $A_{5}$. Then,…
We discuss some physical prospective of the non-BPS effective actions of type IIA and IIB superstring theories. By dealing with the complete all three and four point functions, including a closed string Ramond-Ramond (in terms of both its field strength and its potential), gauge (scalar) fields as well as a real tachyon and under symmetry structures, we find various restricted world volume and bulk Bianchi identities. The complete forms of the non-BPS scattering amplitudes including their Chan-Paton factors are elaborated. All the singularity structures of the non-BPS amplitudes, their all ord…
Recent results on the effective non-local dynamics of the tachyon mode of open string field theory (OSFT) show that approximate solutions can be constructed which obey the diffusion equation. We argue that this structure is inherited from the full theory, where it admits a universal formulation. In fact, all known exact OSFT solutions are superpositions of diffusing surface states. In particular, the diffusion equation is a spacetime manifestation of OSFT gauge symmetries.
