We find explicit expressions for two first finite size corrections to
the
distribution of Bethe roots, the asymptotics of energy and high
conserved
charges in the sl(2) quantum Heisenberg spin chain of length J in the
thermodynamical limit J->\infty for low energies E\sim 1/J. This
limit was
recently studied in the context of integrability in perturbative N=4
super-Yang-Mills theory. We applied the double scaling technique to
Baxter
equation, similarly to the one used for large random matrices near the
edge of
the eigenvalue distribution. The positions of Bethe roots are described
near
the edge by zeros of Airy function. Our method can be generalized to
any order
in 1/J. It should also work for other quantum integrable models.
We generalize the discussion of hep-th/0509170 to charged black holes. For the two dimensional charged black hole, which is described by an exactly solvable worldsheet theory, a transition from the black hole to the string phase occurs when the Hawking temperature of the black hole reaches a limiting value, the temperature of free strings with the same mass and charge. At this point a tachyon winding around Euclidean time in the Euclidean black hole geometry, which has a non-zero condensate, becomes massless at infinity, and the horizon of the black hole is infinitely smeared. For Reissner-Nordstrom black holes in d\ge 4 dimensions, the exact worldsheet CFT is not known, but we propose that it has similar properties. We check that the leading order solution is in good agreement with this proposal, and discuss the expected form of \alpha' corrections.
We consider the most general three-state spin chain with U(1)^3 symmetry and nearest neighbour interaction. Our model contains as a special case the spin chain describing the holomorphic three scalar sector of the three parameter complex deformation of N=4 SYM, dual to type IIB string theory in the generalized Lunin-Maldacena backgrounds discovered by Frolov. We formulate the coordinate space Bethe ansatz, calculate the S-matrix and determine for which choices of parameters the S-matrix fulfills the Yang-Baxter equations. For these choices of parameters we furthermore write down the R-matrix. We find in total four classes of integrable models. In particular, each already known model of the above type is nothing but one in a family of such models.
We construct a classical solution in the GSO(-) sector in the framework of a Wess-Zumino-Witten-like open superstring field theory on a non-BPS D-brane. We use an su(2) supercurrent, which is obtained by compactifying a direction to a circle with the critical radius, in order to get analytical tachyonic lump solutions to the equation of motion. By investigating the action expanded around a solution we find that it represents a deformation from a non-BPS D-brane to a D-brane-anti-D-brane system at the critical value of a parameter which is contained in classical solutions. Although such a process was discussed in terms of boundary conformal field theory before, our study is based on open superstring field theory including interaction terms.
We present a trace formula for an index over the spectrum of four dimensional superconformal field theories on $S^3 \times $ time. Our index receives contributions from states invariant under at least one supercharge and captures all information -- that may be obtained purely from group theory -- about protected short representations in 4 dimensional superconformal field theories. In the case of the $\CN=4$ theory our index is a function of four continuous variables. We compute it at weak coupling using gauge theory and at strong coupling by summing over the spectrum of free massless particles in $AdS_5\times S^5$ and find perfect agreement at large $N$ and small charges. Our index does not reproduce the entropy of supersymmetric black holes in $AdS_5$, but this is not a contradiction, as it differs qualitatively from the partition function over supersymmetric states of the ${\cal N}=4$ theory. We note that entropy for some small supersymmetric $AdS_5$ black holes may be reproduced via a D-brane counting involving giant gravitons. For big black holes we find a qualitative (but not exact) agreement with the naive counting of BPS states in the free Yang Mills theory. In this paper we also evaluate and study the partition function over the chiral ring in the $\CN=4$ Yang Mills theory.
We compute the masses of all moduli in the unstable deSitter vacua arising in the toy model of cosmological M-theory flux compactifications on the G2 holonomy manifolds of [1]. The slow-roll parameters in the tachyonic directions are shown to be too large to be useful for conventional models of inflation. However, it appears that we can find fast roll regimes which could, under certain conditions, account for the current dark energy driven accelerated expansion of the universe.
We describe a modified KKLT mechanism of moduli stabilization in a supersymmetric Minkowski vacuum state. In this mechanism, supersymmetry ensures vacuum stability and positivity of the mass matrix for the dilaton, complex structure, and the volume modulus.
We propose that the state represented by the Nariai black hole inside de Sitter space is the ground state of the de Sitter gravity, while the pure de Sitter space is the maximal energy state. With this point of view, we investigate thermodynamics of de Sitter space, we find that if there is a dual field theory, this theory can not be a CFT in a fixed dimension. Near the Nariai limit, we propose that the dual theory is effectively an 1+1 CFT living on the radial segment connecting the cosmic horizon and the black hole horizon. If we go beyond the de Sitter limit, the "imaginary" high temperature phase can be described by a CFT with one dimension lower than the spacetime dimension. Below the de Sitter limit, we are approaching a phase similar to the Hagedorn phase in 2+1 dimensions, the latter is also a maximal energy phase if we hold the volume fixed.
In Witten's open cubic bosonic string field theory and Berkovits' superstring field theory we investigate solutions representing fundamental strings ending on the D-branes, which correspond to Callan-Maldacena solution in Born-Infeld theory. The solutions are given in order by order manner, and we show some full order properties. In superstring case we show that the solution is 1/2 BPS in full order.
We present some partial results on the general infrared behavior of bulk-critical 1-d quantum systems with boundary. We investigate whether the boundary entropy, s(T), is always bounded below as the temperature T decreases towards 0, and whether the boundary always becomes critical in the IR limit. We show that failure of these properties is equivalent to certain seemingly pathological behaviors far from the boundary. One of our approaches uses real time methods, in which locality at the boundary is expressed by analyticity in the frequency. As a preliminary, we use real time methods to prove again that the boundary beta-function is the gradient of the boundary entropy, which implies that s(T) decreases with T. The metric on the space of boundary couplings is interpreted as the renormalized susceptibility matrix of the boundary, made finite by a natural subtraction.
We describe a new class of instanton effects in string compactifications that preserve only N=1 supersymmetry in four dimensions. As is well-known, worldsheet or brane instantons in such a background can sometimes contribute to an effective superpotential for the moduli of the compactification. We generalize this phenomenon by showing that such instantons can also contribute to new multi-fermion and higher-derivative F-terms in the low-energy effective action. We consider in most detail the example of heterotic compactification on a Calabi-Yau threefold X with gauge bundle V, in which case we study worldsheet instanton effects that deform the complex structure of the moduli space associated to X and V. We also give new, slightly more economical derivations of some previous results about worldsheet instantons in Type IIA Calabi-Yau compactifications.
After a brief review of string and $M$-Theory we point out some deficiencies. Partly to cure them, we present several arguments for ``$F$-Theory'', enlarging spacetime to $(2, 10)$ signature, following the original suggestion of C. Vafa. We introduce a suggestive Supersymmetric 27-plet of particles, associated to the exceptional symmetric hermitian space $E_{6}/Spin^{c}(10)$. Several possible future directions, including using projective rather than metric geometry, are mentioned. We should emphasize that $F$-Theory is yet just a very provisional attempt, lacking clear dynamical principles.
This paper provides a heuristic derivation of how classical gravitational physics in the AdS/CFT correspondence appears from the strong dynamics of the N=4 SYM theory in a systematic way. We do this in a minisuperspace approximation by studying 1/8 BPS configurations. We show that this is related to a gauged matrix quantum mechanics of commuting matrices. We can show that our description matches the semiclassical physics of 1/8 BPS states in supergravity. We also provide a heuristic description of how massive strings appear in the geometry, and how at strong 't Hooft coupling they become local on the five sphere suggesting that they can be realized as a sigma model on a weakly curved background. In the process we also clarify some aspects of 1/2 BPS states. We also have a conjectured realization of some 1/8 BPS giant graviton wave functions in the dynamics, which captures all 1/8 BPS giant gravitons constructed by Mikhailov. This leads to a lot of different topology changes which can be treated heuristically.
We study the dynamics of strongly interacting gauge-theory matter (modelling quark-gluon plasma) in a boost-invariant setting using the AdS/CFT correspondence. Using Fefferman-Graham coordinates and with the help of holographic renormalization, we show that perfect fluid hydrodynamics emerges at large times as the unique nonsingular asymptotic solution of the nonlinear Einstein equations in the bulk. The gravity dual can be interpreted as a black hole moving off in the fifth dimension. Asymptotic solutions different from perfect fluid behaviour can be ruled out by the appearance of curvature singularities in the dual bulk geometry. Subasymptotic deviations from perfect fluid behaviour remain possible within the same framework.
We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U(1) gauge field with gauge coupling g, there is a new ultraviolet scale Lambda=g M_{Pl}, invisible to the low-energy effective field theorist, which sets a cutoff on the validity of the effective theory. Moreover, there is some light charged particle with mass smaller than or equal to Lambda. The bound is motivated by arguments involving holography and absence of remnants, the (in) stability of black holes as well as the non-existence of global symmetries in string theory. A sharp form of the conjecture is that there are always light "elementary" electric and magnetic objects with a mass/charge ratio smaller than the corresponding ratio for macroscopic extremal black holes, allowing extremal black holes to decay. This conjecture is supported by a number of non-trivial examples in string theory. It implies the necessary presence of new physics beneath the Planck scale, not far from the GUT scale, and explains why some apparently natural models of inflation resist an embedding in string theory.
We discuss the 1/N expansion of the free energy of N logarithmically interacted charges in the plane in an external field. For some particular values of the inverse temperature beta this system is equivalent to the eigenvalue version of certain random matrix models, where it is refered to as the "Dyson gas" of eigenvalues. To find the free energy at large N and the 1/N-corrections, we first use heuristic arguments and then confirm the results by solving the loop equation. The results obtained give some new representations of the mathematical objects related to the Dirichlet boundary value problem, complex analysis and spectral geometry of exterior domains. They also suggest interesting links with bosonic field theory on Riemann surfaces, gravitational anomalies and topological field theories.
We study the leading quantum effects in the recently introduced Matrix Big Bang model. This amounts to a study of supersymmetric Yang-Mills theory compactified on the Milne orbifold. We find a one-loop potential that decays near the Big Bang. More surprisingly, the potential decays very rapidly at late times where it appears to be generated by D-brane effects. Usually, general covariance constrains the form of any effective action generated by renormalization group flow. However, the form of our one-loop potential seems to violate these constraints in a manner that suggests a connection between the cosmological singularity and long wavelength, late time physics.
These notes, based on the remarks made at the 23 Solvay Conference, collect several speculative ideas concerning gauge/ strings duality, de Sitter spaces, dimensionality and the cosmological constant.
We carry out a systematic study of correlation functions of momentum modes in the Euclidean c=1 string, as a function of the radius and to all orders in perturbation theory. We obtain simple explicit expressions for several classes of correlators in terms of special functions. The Normal Matrix Model is found to be a powerful calculational tool that computes c=1 string correlators even at finite N. This enables us to obtain a simple combinatoric formula for the 2n-point function of unit momentum modes, which after T-duality determines the vortex condensate. We comment on possible applications of our results to T-duality at c=1 and to the 2d black hole/vortex condensate problem.
A basic problem in gravitational physics is the resolution of spacetime singularities where general relativity breaks down. The simplest such singularities are conical singularities arising from orbifold identifications of flat space, and the most challenging are spacelike singularities inside black holes (and in cosmology). Topology changing processes also require evolution through classically singular spacetimes. I briefly review how a phase of closed string tachyon condensate replaces, and helps to resolve, basic singularities of each of these types. Finally I discuss some interesting features of singularities arising in the small volume limit of compact negatively curved spaces and the emerging zoology of spacelike singularities.
The null-brane space-time provides a simple model of a big crunch/big bang singularity. A non-perturbative definition of M-theory on this space-time was recently provided using matrix theory. We derive the fermion couplings for this matrix model and study the leading quantum effects. These effects include particle production and a time-dependent potential. Our results suggest that as the null-brane develops a big crunch singularity, the usual notion of space-time is replaced by an interacting gluon phase. This gluon phase appears to constitute the end of our conventional picture of space and time.
It has recently been shown that a Hagedorn phase of string gas cosmology can provide a causal mechanism for generating a nearly scale-invariant spectrum of scalar metric fluctuations, without the need for an intervening period of de Sitter expansion. In this paper we compute the spectrum of tensor metric fluctuations (gravitational waves) in this scenario, and show that it is also nearly scale-invariant. However, whereas the spectrum of scalar modes has a small red-tilt, the spectrum of tensor modes has a small blue tilt, unlike what occurs in slow-roll inflation. This provides a possible observational way to distinguish between our cosmological scenario and conventional slow-roll inflation.
We analyze the finite temperature behavior of the Sakai-Sugimoto model, which is a holographic dual of a theory which spontaneously breaks a U(N_f)_L x U(N_f)_R chiral flavor symmetry at zero temperature. The theory involved is a 4+1 dimensional supersymmetric SU(N_c) gauge theory compactified on a circle of radius R with anti-periodic boundary conditions for fermions, coupled to N_f left-handed quarks and N_f right-handed quarks which are localized at different points on the compact circle (separated by a distance L). In the supergravity limit which we analyze (corresponding in particular to the large N_c limit of the gauge theory), the theory undergoes a deconfinement phase transition at a temperature T_d = 1 / 2 \pi R. For quark separations obeying L > L_c = 0.97 * R the chiral symmetry is restored at this temperature, but for L < L_c = 0.97 * R there is an intermediate phase which is deconfined with broken chiral symmetry, and the chiral symmetry is restored at T = 0.154 / L. All of these phase transitions are of first order.
We study the separation between the spin and the charge in the quantum mechanical Pauli model of electrons. For this we employ an ensemble of electrons in a novel, topologically mixed quantum state. Curiously, we find that the spin-charge separation converts the Pauli Hamiltonian into the Hamiltonian of the non-Abelian Georgi-Glashow model, famous for its ability to support magnetic monopoles and to exhibit confinement. Furthermore, we conclude that the independent spin and charge fluctuations can both be described by the Faddeev model which suggests that there is a deep duality between the spin and the charge. The appearance of the Faddeev model also indicates that the fundamental carriers of both spin and charge are knotted solitons. We expect that our results have a wide impact in condensed matter physics from electronics to spintronics. In a much wider context, there may even be a need to develop a novel fundamental theory of Matter.
Motivated by the desire to relate Bethe ansatz equations for anomalous
dimensions found on the gauge theory side of the AdS/CFT correspondence to
superstring theory on AdS_5 x S5 we explore a connection between the asymptotic
S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum
field theory. The latter generalizes the standard ``non-relativistic''
Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic
Heisenberg spin chain and should be related to a limit of superstring effective
action. We find the exact form of the quartic interaction terms in the
generalized LL type action whose quantum
S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin
chain of Beisert, Dippel and Staudacher (BDS). This generalises to all orders
in the 't Hooft coupling an earlier computation of Klose and Zarembo of the
S-matrix of the standard LL model. We also consider a generalization to the
case when the spin chain S-matrix contains an extra ``string'' phase and
determine the exact form of the LL 4-vertex corresponding to the low-energy
limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the
relation between the resulting ``non-relativistic'' non-local action and the
second-derivative string sigma model on R_t x S3. We comment on modifications
introduced by strong-coupling corrections to the AFS phase. We discuss in
detail the SU(2) sector but also present generalizations to the SU(1|1) and
SL(2) sectors (in the BDS case) and comment on larger sectors.
We derive the asymptotic Bethe ansatz (AFS equations) for the string on S^3 x R sector of AdS_5 x S^5 from the integrable nonhomogeneous dynamical spin chain for the string sigma model proposed in GKSV. It is clear from the derivation that AFS equations can be viewed only as an effective model describing a certain regime of a more fundamental inhomogeneous spin chain.
We show that space-time evolution of one-dimensional fermionic systems is described by nonlinear equations of soliton theory. We identify a space-time dependence of a matrix element of fermionic systems related to the {\it Orthogonality Catastrophe} or {boundary states} with the $\tau$-function of the modified KP-hierarchy. The established relation allows to apply the apparatus of soliton theory to the study of non-linear aspects of quantum dynamics. We also describe a {\it bosonization in momentum space} - a representation of a fermion operator by a Bose field in the presence of a boundary state.
We perform a general study of primordial scalar non-Gaussianities in single field inflationary models. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.
We do not know the symmetries underlying string theory. Furthermore, there must exist an inherently quantum, and spacetime independent, formulation of this theory. Independent of string theory, there should exist a description of quantum mechanics which does not refer to a classical spacetime manifold. We propose such a formulation of quantum mechanics, based on noncommutative geometry. This description reduces to standard quantum mechanics, whenever an external classical spacetime is available. However, near the Planck energy scale, self-gravity effects modify the Schrodinger equation to the non-linear Doebner-Goldin equation. Remarkably, this non-linear equation also arises in the quantum dynamics of D0-branes. This suggests that the noncommutative quantum dynamics introduced here is actually the quantum gravitational dynamics of D0-branes, and that automorphism invariance is a symmetry of string theory.
We study aspects of emergent geometry for the case of orbifold superconformal field theories in four dimensions, where the orbifolds are abelian within the AdS/CFT proposal. In particular, we show that the realization of emergent geometry starting from the N=4 SYM theory in terms of a gas of particles in the moduli space of vacua of a single D3 brane in flat space gets generalized to a gas of particles on the moduli space of the corresponding orbifold conformal field theory (a gas of D3 branes on the orbifold space). Our main purpose is to show that this can be analyzed using the same techniques as in the N=4 SYM case by using the method of images, including the measure effects associated to the volume of the gauge orbit of the configurations. This measure effect gives an effective repulsion between the particles that makes them condense into a non-trivial vacuum configuration, and it is exactly these configurations that lead to the geometry of X in the AdS x X dual field theory