Effective String Theory Research Articles

On the spectrum of closedk= 2 flux tubes inD= 2+1 SU(N) gauge theories

We calculate the energy spectrum of a k = 2 flux tube that is closed around a spatial torus, as a function of its length l. We do so for SU(4) and SU(5) gauge theories in 2 space dimensions. We find that to a very good approximation the eigenstates belong to the irreducible representations of the SU(N) group rather than just to its center, ZN. We obtain convincing evidence that the low-lying states are, for l not too small, very close to those of the Nambu-Goto free string theory (in flat space-time). The correction terms appear to be typically of O(1) in appropriate units, much as one would expect if the bosonic string model were an effective string theory for the dynamics of these flux tubes. This is in marked contrast to the case of fundamental flux tubes where such corrections have been found to be unnaturally small. Moreover we find that these corrections appear to be particularly small when the `phonons' along the string have the same momentum, and large when their momentum is opposite. This provides information about the detailed nature of the interactions in the effective string theory. We have searched for, but not found, extra states that would arise from the excitation of the massive modes presumably associated with the non-trivial structure of the flux tube.

ENERGY-MOMENTUM COMPLEXES FOR A STRINGY BLACK HOLE GEOMETRY IN A LOW-ENERGY EFFECTIVE STRING THEORY

The energy and momentum distributions for a four-dimensional, magnetically charged, stringy black hole geometry, in a low-energy effective string theory, are calculated. To this purpose, the energy-momentum complexes of Einstein, Landau-Lifshitz, Weinberg and Møller are applied. It is found that, in all four prescriptions, the momentum distribution vanishes, while the energies obtained differ, but all are functions of the mass, the scalar charge, and the boost parameter.

The confining string beyond the free-string approximation in the gauge dual of percolation

We simulate five different systems belonging to the universality class of the gauge dual of three-dimensional random percolation to study the underlying effective string theory at finite temperature. All the data for the finite temperature string tension, when expressed by means of adimensional variables, are nicely described by a unique scaling function. We calculate the first few terms of the string tension up to order T6 and compare to different theoretical predictions. We obtain unambiguous evidence that the coefficients of T2 and T4 terms coincide with those of the Nambu-Goto string, as expected, while the T6 term strongly differs and is characteristic of the universality class of this specific gauge theory.

Fluctuations of the baryonic flux-tube junction from effective string theory

In quenched QCD, where the dynamic creation of quark-antiquark pairs out of the vacuum is neglected, a confined baryonic system composed of three static quarks exhibits stringlike behavior at large interquark separation, with the formation of flux tubes characterized by the geometry of the so-called $Y$ ansatz. We study the fluctuations of the junction of the three flux tubes, assuming the dynamics to be governed by an effective bosonic string model. We show that the asymptotic behavior of the effective width of the junction grows logarithmically with the distance between the sources, with the coefficient depending on the number of joining strings, on the dimension of spacetime and on the string tension.

Black Holes in the Dilatonic Einstein-Gauss-Bonnet Theory in Various Dimensions. I: -- Asymptotically Flat Black Holes --

We study spherically symmetric, asymptotically flat black hole solutions in the low-energy effective heterotic string theory, which is the Einstein gravity with Gauss-Bonnet term and the dilaton, in various dimensions. We derive the field equations for suitable ansatz for general D dimensions and construct black hole solutions of various masses numerically in D=4,5,6 and 10 dimensional spacetime with (D-2)-dimensional hypersurface with positive constant curvature. A detailed comparison with the non-dilatonic solutions is made. We also examine the thermodynamic properties of the solutions. It is found that the dilaton has significant effects on the black hole solutions, and we discuss physical consequences.

Closed k-strings in SU(N) gauge theories: [formula omitted] dimensions

We calculate the ground state energies of closed k-strings in (2+1)-dimensional SU(N) gauge theories, for N=4,5,6,8 and k=2,3,4. From the dependence of the ground state energy on the string length, we infer that such k-strings are described by an effective string theory that is in the same bosonic universality class (Nambu–Goto) as the fundamental string. When we compare the continuum k-string tensions to the corresponding fundamental string tensions, we find that the ratios are close to, but typically 1–2% above, the Casimir scaling values favoured by some theoretical approaches. Fitting the N-dependence in a model-independent way favours an expansion in 1/N (as in Casimir scaling) rather than the 1/N2 that is suggested by naive colour counting. We also observe that the low-lying spectrum of k-string states falls into sectors that belong to particular irreducible representations of SU(N), demonstrating that the dynamics of string binding knows about the full gauge group and not just about its centre.

Entropy function and universality of entropy-area relation for small black holes

We discuss the entropy-area relation for the small black holes with higher curvature corrections by using the entropy function formalism and field redefinition method. We show that the entropy ${S}_{BH}$ of the small black hole is proportional to its horizon area $A$. In particular, we find a universal result that ${S}_{BH}=A/2G$, the ratio is 2 times of Bekenstein-Hawking entropy-area formula in many cases of physical interest. In four dimensions, the universal relation is always true irrespective of the coefficients of the higher-order terms if the dilaton couplings are the same, which is the case for string effective theory, while in five dimensions, the relation again holds irrespective of the overall coefficient if the higher-order corrections are in the GB combination. We also discuss how this result generalizes to known physically interesting cases with Lovelock correction terms in various dimensions, and possible implications of the universal relation.

SEMICLASSICAL AND QUANTUM BLACK HOLES AND THEIR EVAPORATION, DE SITTER AND ANTI-DE SITTER REGIMES, GRAVITATIONAL AND STRING PHASE TRANSITIONS

An effective string theory in physically relevant cosmological and black hole space–times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and anti-de Sitter AdS space–times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square-root branch point singularity in any space–time dimensions. This is of the type of the de Vega–Sánchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For dS background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition. (iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in nonthermal pure quantum radiation (no information loss). (vi) New lower string bounds are given for the Kerr–Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical–quantum (wave–particle) duality, which is universal irrespective of any symmetry or isommetry of the space–time and of the number or the kind of space–time dimensions.

Continuum limit of string formation in 3d [formula omitted] LGT

We study the continuum limit of the string-like behaviour of flux tubes formed between static quarks and antiquarks in three-dimensional SU(2) lattice gauge theory. We compare our simulation data with the predictions of both effective string models as well as perturbation theory. On the string side we obtain clear evidence for convergence of data to predictions of Nambu–Goto theory. We comment on the scales at which the static potential starts departing from one-loop perturbation theory and then again being well described by effective string theories. We also estimate the leading corrections to the one-loop perturbative potential as well as the Nambu–Goto effective string. In the intermediate regions we find an empirical formula which gives surprisingly good fits. We also compare our results with earlier works.

Accelerating Cosmologies in the Einstein-Gauss-Bonnet Theory with a Dilaton

We study cosmological solutions in low-energy effective heterotic string theory, which consists of the Einstein gravity with the Gauss-Bonnet term and a dilaton. We show that the field equations take the form of an autonomous system for flat internal and external spaces, and we derive all the fixed points in the system. We also examine the time evolution of the solutions and the question of whether the solutions can describe (transient) accelerated expansion of our four-dimensional space in the Einstein frame.

Realizing scale-invariant density perturbations in low-energy effective string theory

We discuss the realization of inflation and resulting cosmological perturbations in the low-energy effective string theory. In order to obtain nearly scale-invariant spectra of density perturbations and a suppressed tensor-to-scalar ratio, it is generally necessary that the dilaton field $\ensuremath{\phi}$ is effectively decoupled from gravity together with the existence of a slowly varying dilaton potential. We also study the effect of second-order corrections to the tree-level action which are the sum of a Gauss-Bonnet term coupled to $\ensuremath{\phi}$ and a kinetic term $(\ensuremath{\nabla}\ensuremath{\phi}{)}^{4}$. We find that it is possible to realize observationally supported spectra of scalar and tensor perturbations provided that the correction is dominated by the $(\ensuremath{\nabla}\ensuremath{\phi}{)}^{4}$ term even in the absence of the dilaton potential. When the Gauss-Bonnet term is dominant, tensor perturbations exhibit violent negative instabilities on small scales about a de Sitter background in spite of the fact that scale-invariant scalar perturbations can be achieved.

Static forces in [formula omitted][formula omitted] gauge theories

Using a three-level algorithm we perform a high-precision lattice computation of the static force up to 1 fm in the ( 2 + 1 ) -dimensional SU ( 5 ) gauge theory. The Sommer parameter r 0 = 0.5 fm is used to set the scale. Discretization errors and the continuum limit are discussed in detail. By comparison with existing SU ( 2 ) and SU ( 3 ) data it is found that σ r 0 2 = 1.65 − π 24 holds at an accuracy of 1% for all N ⩾ 2 . The effective central charge c ( r ) is obtained and an intermediate distance r s is defined via the property c ( r s ) = π 24 . It separates in a natural way the short-distance regime governed by perturbation theory from the long-distance regime described by an effective string theory. The ratio r s / r 0 decreases significantly from SU ( 2 ) to SU ( 3 ) to SU ( 5 ) , where r s < r 0 . We give a preliminary estimate of its value in the large- N limit. The static force in the smallest representation of N -ality 2, which tends to the k = 2 string tension as r → ∞ , is also computed up to 0.7 fm. The deviation from Casimir scaling is positive and grows from 0.1% to 1% in that range.

NoncommutativeD3-brane, black holes, and attractor mechanism

We revisit the $4D$ generalized black hole geometries, obtained by us [14], with a renewed interest, to unfold some aspects of effective gravity in a noncommutative ${D}_{3}$-brane formalism. In particular, we argue for the existence of extra dimensions in the gravity decoupling limit in the theory. We show that the theory is rather described by an ordinary geometry and is governed by an effective string theory in $5D$. The extremal black hole geometry ${\mathrm{AdS}}_{5}$ obtained in effective string theory is shown to be in precise agreement with the gravity dual proposed for ${D}_{3}$-brane in a constant magnetic field. Kaluza-Klein compactification is performed to obtain the corresponding charged black hole geometries in $4D$. Interestingly, they are shown to be governed by the extremal black hole geometries known in string theory. The attractor mechanism is exploited in effective string theory underlying a noncommutative ${D}_{3}$-brane and the macroscopic entropy of a charged black hole is computed. We show that the generalized black hole geometries in a noncommutative ${D}_{3}$-brane theory are precisely identical to the extremal black holes known in $4D$ effective string theory.

Coupling hybrid inflation to moduli

Hybrid inflation can be realized in low energy effective string theory, asdescribed using supergravity. We find that the coupling of moduli toF-term hybrid inflation in supergravity leads to a slope and a curvature for the inflaton potential. Theϵ and η parameters receive contributions at tree and one loop level which are not compatible withslow roll inflation. Furthermore the coupling to the moduli sector can even preventinflation from ending at all. We show that introducing shift symmetries in theinflationary sector and taking the moduli sector to be no-scale removes mostof these problems. If the moduli fields are fixed during inflation, as is usuallyassumed, it appears that viable slow roll inflation can then be obtained with just onefine-tuning of the moduli sector parameters. However, we show this is not a reasonableassumption, and that the small variation of the moduli fields during inflation gives asignificant contribution to the effective inflaton potential. This typically implies thatη≈−6, although it may be possible to obtain smaller values with heavy fine-tuning.

Poincaré invariance in effective string theories

We investigate the dispersion relation of the winding closed-string states in SU(N) gauge theory defined on a d-dimensional hypertorus, in a class of effective string theories. We show that order by order in the asymptotic expansion, each energy eigenstate satisfies a relativistic dispersion relation. This is illustrated in the Luscher-Weisz effective string theory to two-loop order, where the Polyakov loop matrix elements between the vacuum and the closed string states are obtained explicitly. We attempt a generalization of these considerations to the case of compact dimensions transverse to the string.

Quantum cosmology: expectations and results

We study cosmologies based on low-energy effective string theory with higher-order string corrections to a tree-level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre-Big-Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre-Big-Bang and Ekpyrotic models. We also discuss the effect of higher-order string corrections on a dark energy universe and show several interesting possibilities of the avoidance of future singularities.

Cosmologies from higher‐order string corrections

AbstractWe study cosmologies based on low‐energy effective string theory with higher‐order string corrections to a tree‐level action and with a modulus scalar field (dilaton or compactification modulus). In the presence of such corrections it is possible to construct nonsingular cosmological solutions in the context of Pre‐Big‐Bang and Ekpyrotic universes. We review the construction of nonsingular bouncing solutions and resulting density perturbations in Pre‐Big‐Bang and Ekpyrotic models. We also discuss the effect of higher‐order string corrections on a dark energy universe and show several interesting possibilities of the avoidance of future singularities.

InfiniteNphase transitions in continuum Wilson loop operators

We define smoothed Wilson loop operators on a four dimensional lattice and check numerically that they have a finite and nontrivial continuum limit. The continuum operators maintain their character as unitary matrices and undergo a phase transition at infinite N reflected by the eigenvalue distribution closing a gap in its spectrum when the defining smooth loop is dilated from a small size to a large one. If this large N phase transition belongs to a solvable universality class one might be able to calculate analytically the string tension in terms of the perturbative Lambda-parameter. This would be achieved by matching instanton results for small loops to the relevant large-N-universal function which, in turn, would be matched for large loops to an effective string theory. Similarities between our findings and known analytical results in two dimensional space-time indicate that the phase transitions we found only affect the eigenvalue distribution, but the traces of finite powers of the Wilson loop operators stay smooth under scaling.

The partition function of interfaces from the Nambu-Goto effective string theory

We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.

Dark energy and cosmological solutions in second-order string gravity

We study the cosmological evolution based on a D-dimensional action in low-energy effective string theory in the presence of second-order curvature corrections and a modulus scalar field (a dilaton or compactification modulus). A barotropic perfect fluid coupled to the scalar field is also allowed. Phase space analysis and the stability of asymptotic solutions are performed for a number of models which include (i) a fixed scalar field, (ii) a linear dilaton in the string frame, and (iii) a logarithmic modulus in the Einstein frame. We confront analytical solutions with observational constraints for the deceleration parameter and show that Gauss–Bonnet gravity alone (i.e., with no matter fields) may not explain the current acceleration of the universe. We also study the future evolution of the universe using the Gauss–Bonnet parametrization and find that big rip singularities can be avoided even in the presence of a phantom fluid because of the balance between the fluid and curvature corrections. A non-minimal coupling between the fluid and the modulus field also opens up the interesting possibility of avoiding a big rip regardless of the details of the fluid equation of state.