Massive String Modes Research Articles

27aXB-8 Massive String Modes in Holographic QCD

27aXB-8 Massive String Modes in Holographic QCD

Mesons as Open Strings in a Holographic Dual of QCD

We study meson spectrum obtained from massive open string modes in a holographic dual of QCD constructed on the basis of a D4/D8-brane configuration in type IIA string theory. The spectrum includes mesons with spin higher than one. Taking into account the effect of curved background perturbatively, we obtain a mass formula for these mesons, which exhibits the linear Regge behavior at the leading order with subleading non-linear corrections. We argue that the string spectrum captures some features of the observed meson spectrum. For example, a_2(1320), b_1(1235), \pi(1300), a_0(1450), etc., are identified as the first excited massive open string states and \rho_3(1690), \pi_2(1670), etc., are identified as the second excited states.

QUANTUM STRINGS IN AdS5 × S5 AND GAUGE–STRING DUALITY

We review some recent progress in understanding the spectrum of energies/dimensions of strings/operators in AdS5 × S5 – planar [Formula: see text] super Yang-Mills correspondence. We consider leading strong coupling corrections to the energy of lightest massive string modes in AdS5 × S5, which should be dual to members of the Konishi operator multiplet in the SYM theory. This determines the general structure of strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for semiclassical string states to extract information about the leading coefficients in this expansion.

Quantum strings inAdS5×S5: strong-coupling corrections to dimension of Konishi operator

We consider leading strong coupling corrections to the energy of the lightest massive string modes in AdS_5 x S^5, which should be dual to members of the Konishi operator multiplet in N=4 SYM theory. This determines the general structure of the strong-coupling expansion of the anomalous dimension of the Konishi operator. We use 1-loop results for several semiclassical string states to extract information about the leading coefficients in this expansion. Our prediction is Delta= 2 lambda^{1/4} + b_0 + b_1 lambda^{-1/4} + b_3 lambda^{-3/4} +..., where b_0 and b_1 are rational while b_3 is transcendental containing zeta(3). Explicitly, we argue that b_0= Delta_0 - 4 (where Delta_0 is the canonical dimension of the corresponding gauge-theory operator in the Konishi multiplet) and b_1=1. Our conclusions are sensitive to few assumptions, implied by a correspondence with flat-space expressions, on how to translate semiclassical quantization results into predictions for the exact quantum string spectrum.

Noncommutative geometry, quantum effects and DBI-scaling in the collapse of D0-D2 bound states

We study fluctuations of time-dependent fuzzy two-sphere solutions of the non-abelian DBI action of D0-branes, describing a bound state of a spherical D2-brane with N D0-branes. The quadratic action for small fluctuations is shown to be identical to that obtained from the dual abelian D2-brane DBI action, using the non-commutative geometry of the fuzzy two-sphere. For some of the fields, the linearized equations take the form of solvable Lam\'e equations. We define a large-N DBI-scaling limit, with vanishing string coupling and string length, and where the gauge theory coupling remains finite. In this limit, the non-linearities of the DBI action survive in both the classical and the quantum context, while massive open string modes and closed strings decouple. We describe a critical radius where strong gauge coupling effects become important. The size of the bound quantum ground state of multiple D0-branes makes an intriguing appearance as the radius of the fuzzy sphere, where the maximal angular momentum quanta become strongly coupled.

Bethe Ansatz for Quantum Strings

We propose Bethe equations for the diagonalization of the Hamiltonian of quantum strings on AdS_5 x S^5 at large string tension and restricted to certain large charge states from a closed su(2) subsector. The ansatz differs from the recently proposed all-loop gauge theory asymptotic Bethe ansatz by additional factorized scattering terms for the local excitations. We also show that our ansatz quantitatively reproduces everything that is currently known about the string spectrum of these states. Firstly, by construction, we recover the integral Bethe equations describing semiclassical spinning strings. Secondly, we explain how to derive the 1/J energy corrections of arbitrary M-impurity BMN states, provide explicit, general formulae for both distinct and confluent mode numbers, and compare to asymptotic gauge theory. In the special cases M=2,3 we reproduce the results of direct quantization of Callan et al. Lastly, at large string tension and relatively small charge we recover the famous 2 (n^2 lambda)^(1/4) asymptotics of massive string modes at level n. Remarkably, this behavior is entirely determined by the novel scattering terms. This is qualitatively consistent with the conjecture that these terms occur due to wrapping effects in gauge theory. Our finding does not in itself cure the disagreements between gauge and string theory, but leads us to speculate about the structure of an interpolating Bethe ansatz for the AdS/CFT system at finite coupling and charge.

Exotic Tensor Gauge Theory and Duality

Gauge fields in exotic representations of the Lorentz group in D dimensions - i.e. ones which are tensors of mixed symmetry corresponding to Young tableaux with arbitrary numbers of rows and columns - naturally arise through massive string modes and in dualising gravity and other theories in higher dimensions. We generalise the formalism of differential forms to allow the discussion of arbitrary gauge fields. We present the gauge symmetries, field strengths, field equations and actions for the free theory, and construct the various dual theories. In particular, we discuss linearised gravity in arbitrary dimensions, and its two dual forms.

On off-shell structure of open string sigma model

We analyze several problems related to off-shell structure of open string sigma model by using a combination of derivative expansion and expansion in powers of the fields. According to the sigma model approach to bosonic open string theory, the tachyon effective action $S(T)$ coincides with the renormalized partition function $Z(T)$ of sigma model on a disk, up to a term vanishing on shell. On the other hand, $Z(T)$ is a generating functional of perturbative open string scattering amplitudes. If $S(T) = Z(T)$, then there should be no contribution of exchange diagrams to string amplitudes computed using $S(T)$. We compute the cubic term in the effective action, and show that it vanishes if some but not all external legs are on shell, and, therefore, any exchange diagram involving the cubic term vanishes too. Then, we discuss a problem of turning on nonrenormalizable boundary interactions, corresponding to massive string modes. We compute the quadratic term for a symmetric tensor field, and show that despite nonrenormalizability of the model one can consistently remove all divergent terms, and obtain a quadratic action reproducing the on-shell condition for the field. We also briefly discuss fermionic (NS) sigma model, compute the tachyon quadratic term, and show that it reproduces the correct tachyon mass. We note that turning on a massive symmetric tensor field leads to the appearance of a term linear in it, which can be removed by adding a higher-derivative term to the boundary of the disc.

Contact interactions in D-brane models

We compute the tree-level four-point scattering amplitudes in string models where matter fields live on D-brane intersections. Extracting the contribution of massless modes, we are left with dimension-six four-fermion operators which in general receive contributions from three different sources: exchange of massive Kaluza--Klein excitations, winding modes and string oscillator states. We compute their coefficients and extract new bounds on the string scale in the brane-world scenario. This is contrasted with the situation where matter fields arise from open strings with both ends confined on the same collection of D-branes, in which case the exchange of massive string modes leads to dimension-eight operators that have been studied in the past. When matter fields live on brane intersections, the presence of dimension-six operators increases the lower bound on the string scale to 2--3 TeV, independently of the number of large extra dimensions.

Massive string modes and non-singular pre-big-bang cosmology

Perturbative α′ corrections to the low energy string effective action have been recently found to have a potentially regularizing effect on the singularity of the lowest order pre-big-bang solutions. Whether they actually regularize it, however, cannot be determined working at any finite order in a perturbative expansion in powers of the string constant α′, because of scheme dependence ambiguities. Physically, these corrections are dominated by the integration over the first few massive string states. Very massive string modes, instead, can have a regularizing effect which is non-perturbative in α′ and which basically comes from the fact that in a gravitational field with Hubble constant H they are produced with an effective Hawking temperature T = H/(2 π), and an infinite production rate would occur if this temperature exceeded the Hagedorn temperature. We discuss technical and conceptual difficulties of this non-perturbative regularization mechanism.

Dilaton, antisymmetric tensor and gauge fields in string effective theories at the one-loop level

We investigate the dependence of the gauge couplings on the dilation field in string effective theories at the one-loop level. First we resolve the discrepancies between statements based on symmetry considerations and explicit calculations in string effective theories on this subject. A calculation of the relevant one-loop scattering amplitudes in string theory gives us further information and allows us to derive the exact form of the corresponding effective lagrangian. In particular there is no dilaton dependent one-loop correction to the holomorphic f - function arising from massive string modes in the loop. In addition we address the coupling of the antisymmetric tensor field to the gauge bosons at one loop. While the string S-matrix elements are not reproduced using the usual supersymmetric lagrangian with the chiral superfield representation for the dilaton field, the analogue lagrangian with the dilaton in a linear multiplet naturally gives the correct answer.

Spacetime supersymmetry of extended fermionic strings in 2+2 dimensions

The N=2 fermionic string theory is revisited in the light of its recently proposed equivalence to the non-compact N=4 fermionic string model. The issues of spacetime Lorentz covariance and supersymmetry for the BRST quantized N=2 strings living in uncompactified 2+2 dimensions are discussed. The equivalent local quantum supersymmetric field theory appears to be the most transparent way to represent the spacetime symmetries of the extended fermionic strings and their interactions. The considerations support Siegel's (1992) ideas about the presence of SO(2,2) Lorentz symmetry as well as at least two self-dual spacetime supersymmetries in the theory of N=2(4) fermionic strings, though the authors do not have a compelling reason to argue for the necessity of maximal spacetime supersymmetry. The worldsheet arguments for the absence of all massive string modes in the physical spectrum and the vanishing of all string-loop amplitudes in the Polyakov (1981) approach, are given on the basis of the general consistency of the theory.

Duality-invariant partition functions and automorphic superpotentials for (2,2) string compactifications

We define the topological free energy for string compactifications, which is relevant for the discussion of perturbative as well as non-perturbative effects in string theory. This modulidependent functional, originating from the integration over massive string modes, is determined by automorphic functions of the target-space duality group. We explicitly construct these automorphic functions for symmetric orbifold and Calabi-Yau compactifications.

ON THE RENORMALIZATION GROUP APPROACH TO STRING EQUATIONS OF MOTION

We discuss the program of deriving the string field theory equations of motion for all (massless and massive) string modes as the renormalization group fixed point equations for the most general sigma model containing all possible ("nonrenormalizable") interactions. We review the approach based on the Wilson RG equation and point out the problem of cutoff dependence of the interaction term in the corresponding "quadratic" beta function. The relation between the sigma model path integral and the string scattering amplitudes is clarified. We suggest a new approach to the derivation of the generalized sigma model beta functions in which the central role is played by the condition of completeness of the set of interaction terms ("vertex opeators") present in the sigma model action. The use of the completeness relation makes it possible to obtain closed expressions for the sigma model partition function and the beta functions. The resulting beta functions contain all higher powers of the couplings (fields).

String field equations and the dual s-matrix from the exact renormalization group

We investigate explicitly the variation, with respect to the Liouville mode α, of the Polyakov path integral corresponding to the closed bosonic string, including sources for all massless and massive string modes. Global conformal invariance is seen to imply a set of equations of motion for these sources, which we derive in closed form. The consideration of non-trivial backgrounds requires one to carry out a renormalization procedure, which generates renormalization type equations valid away from the conformal point. In the trivial vacuum the equations of motion involve just a bilinear interaction term which is closely related to operator product coefficients. The iterative solution to these equations allows us to construct the dual S-matrix.

Entropy production in a non‐conservative gravitational theory

AbstractThe production of entropy is calculated in a Friedman Universe governed by a non‐conservative gravitational theory permitting the creation of matter. The calculation has two motivations, the first is that it represents a mechanism to generate the large entropy per baryon observed, and secondly, it simulates the ten dimensional mechanism for entropy production by the out‐of‐equilibrium condition between massive string modes and massless modes with the added condition of energy non‐conservative gravitation.

Thermodynamics of higher dimensional black holes

We discuss the thermodynamics of higher dimensional black holes with particular emphasis on a new class of spinning black holes which, due to the increased number of Casimir invariants, have additional spin degrees of freedom. In suitable limits, analytic solutions in arbitrary dimensions are presented for their temperature, entropy, and specific heat. In 5 + 1 and 9 + 1 dimensions, more general forms for these quantities are given. It is shown that the specific heat for a higher dimensional black hole is negative definite if it has only one non-zero spin parameter, regardless of the value of this parameter. We also consider equilibrium configurations with both massless particles and massive string modes.

Does string theory solve the puzzles of black hole evaporation?

We point out that the massive modes of closed superstring theories may play a crucial role in the last stages of black hole evaporation. If the Bekenstein-Hawking entropy describes the true degeneracy of a black hole — implying loss of quantum coherence and the unitary evolution of quantum states-it becomes entropically favorable for an evaporating black hole to make a transition to a state of massive string modes. This in turn may decay into massless modes of the string (radiation) avoiding the naked singularity exposed by black hole evaporation in the semiclassical picture. Alternatively, quantum coherence may be maintained if the entropy of an evaporating black hole is much larger than that given by the Bekenstein-Hawking formula. In that case, however, the transition to massive string modes is unlikely. String theories might thus resolve the difficulty of the naked singularity, but it appears likely that they will still involve loss of quantum coherence.

On the effective potential and gravitino mass determination in compactified superstring models

The one-loop effective potential is computed in a class of no-scale models proposed as the low-energy limit of ten-dimensional superstrings compactified on a Calabi-Yau manifold. As regularization prescriptions both a cut-off over integration momenta and n subtractions ( n ⩾ 2) are used. In all cases the effective potential is a monotonically decreasing function of the gravitino mass. It is suggested that massive string modes and/or non-perturbative effects on the string could stabilize the potential.

Role of string excitation in the last stages of black-hole evaporation.

We argue that the massive modes of the superstring can play an important role in the last stages of black-hole evaporation. If the Bekenstein-Hawking entropy is the true statistical entropy of an evaporating black hole, it becomes probable for a black hole to disappear by making a transition to an excited string state. This excited string state can then decay to massless radiation, avoiding the naked singularity of the semiclassical picture. We also construct the energy-volume phase diagram separating the three phases: pure radiation, black hole and radiation, and massive string modes and radiation.