We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in alpha prime, using Wald's formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, but the formalism picks up only one of them to play a role in the first law.
This work is a first step towards the derivation of the first law at first order in alpha prime where, more complicated, non-Abelian, Lorentz ("gravitational") and Yang-Mills Chern-Simons terms are included in the Kalb-Ramond field strength. The derivation of a first law is a necessary step towards the derivation of a manifestly gauge-invariant entropy formula which is still lacking in the literature. In its turn, this entropy formula is needed to compare unambiguously macroscopic and microscopic black hole entropies.
We derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action to first order in alpha prime using Wald's formalism. We carefully take into account all the symmetries of the theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant entropy formula in which all the terms can be computed explicitly. An entropy formula with these properties allows unambiguous calculations of macroscopic black-hole entropies to first order in alpha prime that can be reliably used in a comparison with the microscopic ones. Such a formula was still lac…
We construct solitonic string solutions of N=2 four-dimensional heterotic models of rank three, four and five. These finite energy configurations have constant dilaton while the moduli fields vary over space-time with jumps at the location of the string cores consistent with the T-duality groups SL(2,Z), SL(2,Z) X SL(2,Z) and Sp(4,Z). The solutions are expressed in terms of modular forms of the T-duality group. They break half of the supersymmetries and the vacuum contain a certain number of solitonic strings in order the singularities to be resolved in a Ricci flat way.
We discuss heterotic string theories in two dimensions with gauge groups Spin(24) and Spin(8) x E_8. After compactification the theories exhibit a rich spectrum of states with both winding and momentum. At special points some of these stringy states become massless, leading to new first order phase transitions. For example, the thermal theories exhibit standard thermodynamics below the phase transition, but novel and peculiar behavior above it. In particular, when the radius of the Euclidean circle is smaller than the phase transition point the torus partition function is not given by the ther…
We study the first-order in $α'$ corrections to 4-charge black holes (with the Reissner-Nordström black hole as a particular example) beyond the near-horizon limit in the Heterotic Superstring effective action framework. The higher-curvature terms behave as delocalized sources in the equations of motion and in the Bianchi identity of the 3-form. For some charges, this introduces a shift between their values measured at the horizon and asymptotically. Some of these corrections and their associated charge shifts, but not all of them, can be canceled using appropriate SU$(2)$ instantons for the h…
The structure of stringy quantum corrections to four-dimensional effective theories is particularly interesting for string phenomenology and attempts to stabilize moduli. We consider the heterotic string compactified on a Calabi-Yau space. For this case, we compute the leading corrections to the kinetic terms of moduli fields. The structure of these corrections is largely dictated by the underlying higher-dimensional extended supersymmetry. We find corrections generically of order (alpha')^2 rather than of order (alpha')^3 found in type II compactifications or heterotic compactifications with …
Closed string theories on orbifolds contain both untwisted and twisted states. The latter are normally assumed to live exactly at the orbifold fixed points. We perform a calculation of a gauge field tadpole amplitude and show that off-shell both the twisted and untwisted states give rise to non-trivial momentum profiles over the orbifold C^3/Z_3. These profiles take the form of Gaussian distributions integrated over the fundamental domain of the modular parameter of the torus. The propagators of the internal coordinate fields on the torus world sheet determine the width of the Gaussian profile…
We search for $N=2$, $d=4$ theories which can be realized both as heterotic string compactifications on $K_{3}\times T^{2}$ and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative superpotential of one string theory is given in terms of tree level computations in the other string theory. In particular we find concrete examples which provide the stringy realization of the results of Seiberg and Witten on N=2 Yang-Mills theory, corrected by gravitational/stringy effects. We also discuss some examples which shed light on how the moduli spaces of…
We explicitly analyse $O(α')$ corrections to heterotic supergravity on toroidal orbifolds and their resolutions, which play important roles in string phenomenology as well as moduli stabilisation. Using a conformal factor ansatz that is valid only for four dimensional geometries, we obtain a closed expression for the $O(α')$ metric corrections in the case of several orbifold limits of K3, namely $T^4/\mathbb{Z}_n$ where $n=2,3,4,6$. However, we find that non-standard embedding requires the inclusion of five-branes on such orbifolds. We also numerically investigate the behaviour around orbifold…
We investigate the stability of charged black holes in two-dimensional heterotic string theories that were recently discussed by McGuidan, Nappi and Yost. In the framework of small time-dependent perturbation, we find that these black holes are linearly stable.
We present a static multi-center magnetic solution of toroidally compactified heterotic string theory, which is T-duality covariant. The space-time geometry depends on the mass M and on the O(6,22)-norm N of the magnetic charges. For different range of parameters (M,N)-solution includes 1) two independent positive parameters extremal magnetic black holes with non-singular geometry in stringy frame ($a=1$ black holes included), 2) $a=\sqrt 3$ extremal black holes, 3) singular massive and massless magnetic white holes (repulsons). The electric multi-center solution is also given in an O(6,22)-sy…
Extreme magnetic dilaton black holes are promoted to exact solutions of heterotic string theory with unbroken supersymmetry. With account taken of alpha' corrections this is accomplished by supplementing the known solutions with SU(2) Yang-Mills vectors and scalars in addition to the already existing Abelian U(1) vector field. The solution has a simple analytic form and includes multi-black-holes. The issue of exactness of other black-hole-type solutions, including extreme dilaton electrically charged black holes and Taub-NUT solutions is discussed.
We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O(d,d+G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of…
This work addresses spherically symmetric, static black holes in higher-derivative stringy gravity. We focus on the curvature-squared correction to the Einstein-Hilbert action, present in both heterotic and bosonic string theory. The string theory low-energy effective action necessarily describes both a graviton and a dilaton, and we concentrate on the Callan-Myers-Perry solution in d-dimensions, describing stringy corrections to the Schwarzschild geometry. We develop the perturbation theory for the higher-derivative corrected action, along the guidelines of the Ishibashi-Kodama framework, foc…
Static spherically symmetric asymptotically flat particle-like and black hole solutions are constructed within the SU(2) sector of 4-dimensional heterotic string effective action. They separate topologically distinct Yang-Mills vacua and are qualitatively similar to the Einstein-Yang-Mills spha- lerons and non-abelian black holes discussed recently. New solutions possess quantized values of the dilaton charge.
Two classes of stringy instanton effects, stronger than standard field theory instantons, are identified in the heterotic string theory. These contributions are established using type IIA/heterotic and type I/heterotic dualities. They provide examples for the heterotic case of the effects predicted by Shenker based on the large-order behavior of perturbation theory. The corrections vanish as the radius of the compactification goes to infinity. For appropriate amplitudes, they are computable worldsheet or worldline instanton effects on the dual side. Some potential applications are discussed.
We construct a four-dimensional BPS saturated heterotic string solution from the Taub-NUT solution. It is a non-extremal black hole solution since its Euler number is non-zero. We evaluate its black hole entropy semiclassically. We discuss the relation between the black hole entropy and the degeneracy of string states. The entropy of our string solution can be understood as the microscopic entropy which counts the elementary string states without any complications.
We review recent results on string coupling selection rules for heterotic orbifolds, derived using conformal field theory. Such rules are the first step towards understanding the viability of the recently obtained compactifications with potentially realistic particle spectra. They arise from the properties of the worldsheet instantons that mediate the couplings, and include stringy effects that would seem 'miraculous' to an effective field theory observer.
We study the thermodynamical and geometrical behaviour of the black holes that arise as solutions of the heterotic string action. We discuss the near-horizon scaling behaviour of the solutions that are described by two-dimensional Anti-de Sitter Space AdS(2). We find that finite-energy excitations of AdS(2) are suppressed only for scaling limits characterised by a dilaton which is constant near the horizon, whereas this suppression does not occur when the dilaton is non constant.
We study the first-order $α'$ corrections to the singular 4-dimensional massless stringy black holes studied in the nineties in the context of the Heterotic Superstring. We show that the $α'$ corrections not only induce a non-vanishing mass and give rise to an event horizon, but also eliminate the singularity giving rise to a regular spacetime whose global structure includes further asymptotically flat regions in which the spacetime's mass is positive or negative. We study the timelike and null geodesics and their effective potential, showing that the spacetime is geodesically complete. We dis…
We study the BPS black hole solutions of the (truncated) action for heterotic string theory compactified on a six-torus. The O(3,Z) duality symmetry of the theory, together with the bound state interpretation of extreme black holes, is used to generate the whole spectrum of the solutions. The corresponding spacetime structures, written in terms of the string metric, are analyzed in detail. In particular, we show that only the elementary solutions present naked singularities. The bound states have either null singularities (electric solutions) or are regular (magnetic or dyonic solutions) with …
We examine the two-dimensional spacetimes that emerge from string theory. We find all the solutions with no tachyons, and show that the only non-trivial solution is the black hole spacetime. We examine the role of duality in this picture. We then explore the thermodynamics of these solutions which is complicated by the fact that only in two spacetime dimensions is it impossible to redefine the dilaton field in terms of a canonical scalar field. Finally, we extend our analysis to the heterotic string, and briefly comment on exact, as opposed to perturbative, solutions.
We describe heterotic string and M-theory realizations of the Randall-Sundrum (RS) scenario with $\cx N=2$ and $\cx N=1$ supersymmetry in the bulk. Supersymmetry can be broken only on the world brane, a scenario that has been proposed to account for the smallness of the cosmological constant. An interesting prediction from string duality is the generation of a warp factor for conventional type II Calabi--Yau 3-fold compactifications. On the other hand we argue that an assumption that is needed in the RS explanation of the hierarchy is hard to satisfy in the string theory context.
Static spherically symmetric asymptotically flat charged black hole solutions are constructed within the magnetic SU(3) sector of the 4-dimensional heterotic string effective action. They possess non-abelian hair in addition to the Coulomb magnetic field and are qualitatively similar to the Einstein-Yang-Mills colored SU(3) black holes except for the extremal case. In the extremality limit the horizon shrinks and the resulting geometry around the origin coincides with that of an extremal abelian dilatonic black hole with magnetic charge. Non-abelian hair exibits then typical sphaleron structur…
We study the global structure of vacua of heterotic strings compactified on orbifolds $T^4/Z_N$ (N=2,3) in the presence of heterotic 5-branes. Gauge symmetry breaking associated with orbifold is described by instantons in the field theory. Phase transition between small instantons and heterotic 5-branes provides top-down, stringy account to the spectrum and modular invariance condition. Also it takes us from one vacuum to another by emitting and absorbing instantons. This means that many vacua with different gauge theory are in fact connected and are inherited from perturbative vacua. It follo…
We review recent results on near-horizon static black hole solutions and entropy in R^2-corrected N=2 SUGRA in D=5, focusing on actions connected to heterotic string compactified on K3\times S^1. Comparison with α'-perturbative results, results obtained by using simple Gauss-Bonnet R^2-correction, OSV conjecture and microscopic stringy description (for small black holes) shows that situation in D=5 is, in a sense, even more interesting then in D=4.
Chameleon fields are quantum fields with an increasing mass as a function of the matter density of the environment. Recently chameleon fields have been exploited to solve the cosmological constant problem in the Modified Fujii's Model - MFM [Phys Rev D82 (2010) 044006]. However, gravity has been treated basically at a semiclassical level in that paper. In this article the stringy origin of the MFM is further discussed: as we will see, the MFM can be obtained from heterotic-M-theory. Consequently, a quantum description of gravity is obtained and the theory is finite because we choose the string…
Recent work has provided a direct string calculation of the internal coordinate dependence of gauge field tadpoles on the orbifold C^3/Z_3. We investigate the structure of these profiles in momentum and coordinate space representations using both analytical and numerical methods. The twisted states are determined to be localized within a few string lengths of the singularity. This provides an example of how delta-like singularities, which are typical for field theories on orbifolds, are avoided in string theory. A systematic expansion of the full string result allows us to speculate on how the…
We derive exact relations to all orders in the $α'$ expansion for the charges of a bound system of heterotic strings, solitonic 5-branes and, optionally, a Kaluza-Klein monopole. The expressions, which differ from those of the zeroth-order supergravity approximation, coincide with the values obtained when only the corrections of quadratic order in curvature are included. Our computation relies on the consistency of string theory as a quantum theory of gravity; the relations follow from the matching of the Wald entropy with the microscopic degeneracy. In the heterotic frame, the higher-curvatur…
Motivated by gauge/gravity group in the low energy effective theory of the heterotic string theory and novel aspects of massive gravity in the context of lattice physics, the minimal coupling of Gauss-Bonnet-massive gravity with Born-Infeld electrodynamics is considered. At first, the metric function is calculated and then the geometrical properties of the solutions are investigated. It is found that there is an essential singularity at the origin and the intrinsic curvature is regular elsewhere. In addition, the effects of massive parameters are studied and black hole solutions with multi hor…
A mild version of the weak gravity conjecture (WGC) states that extremal black holes have charge-to-mass ratio larger or equal than one when higher-curvature interactions are taken into account. Since these corrections become more relevant in the low-mass regime, this would allow the decay of extremal black holes in terms of energy and charge conservation. Evidence in this direction has been mainly given in the context of corrections to Einstein-Maxwell theory. Here we compute corrections to the charge-to-mass ratio of some dyonic extremal black holes explicitly embedded in the heterotic strin…
We calculate alpha'^2-corrections to the entropy of the 5-dimensional 3-charge and the 4-dimensional 4-charge large extremal black holes using the low energy effective action of the heterotic string theory. In the 4-dimensional case, our results are in agreement with the microscopic statistical entropy both for the BPS and the non-BPS black holes. In the more interesting 5-dimensional case, where the direct microscopic stringy description is still unknown, our results for the BPS black holes are in agreement with the results obtained from the action supplemented with R^2-correction obtained by…
We interpret reported hints of a Standard Model Higgs boson at ~ 125 GeV in terms of high-scale supersymmetry breaking with a shift symmetry in the Higgs sector. More specifically, the Higgs mass range suggested by recent LHC data extrapolates, within the (non-supersymmetric) Standard Model, to a vanishing quartic Higgs coupling at a UV scale between 10^6 and 10^18 GeV. Such a small value of lambda can be understood in terms of models with high-scale SUSY breaking if the Kahler potential possesses a shift symmetry, i.e., if it depends on H_u and H_d only in the combination (H_u+\bar{H}_d). Thi…
G. Física CAB-CNEA, Centro Atómico Bariloche（CAB-CNEA 物理组，巴里洛切原子中心）；Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（国家科学研究委员会）；Instituto Balseiro, Universidad Nacional de Cuyo (UNCUYO)（巴尔塞罗研究所，门多萨国立大学）
Using dyonic solutions in the type IIA superstring theory on Calabi-Yau manifolds, we reconsider the study of black objects and quantum information theory using string/string duality in six dimensions. Concretely, we relate four-qubits with a stringy quaternionic moduli space of type IIA compactification associated with a dyonic black solution formed by black holes (BH) and black 2-branes (B2B) carrying 8 electric charges and 8 magnetic charges. This connection is made by associating the cohomology classes of the heterotic superstring on T^{4} to four-qubit states. These states are interpreted…
We revisit the four-dimensional theory of gravity that arises from string theory with higher-derivative corrections. By compactifying and truncating the ten-dimensional effective action of heterotic string theory at first order in $α'$, and carefully dealing with field redefinitions, we show that the four-dimensional theory takes the form of an axidilaton model where the scalars couple to the Gauss-Bonnet and Pontryagin densities. Thus, the actual string gravity is a generalization of the well-studied Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons models. Using this action we compute…
Following the work of Sen, we consider the correspondence between extremal black holes and string states in the context of the entropy. We obtain and study properties of electrically charged black hole backgrounds of tree level heterotic string theory compactified on a $p$ dimensional torus, for $D=(10-p)=4 \ldots 9$. We study in particular a one--parameter extremal class of these black holes, the members of which are shown to be supersymmetric. We find that the entropy of such an extremal black hole, when calculated at the stringy stretched horizon, scales in such a way that it can be identif…
We consider, in 5 dimensions, the low energy effective action induced by heterotic string theory including the leading stringy correction of order alpha'. In the presence of a single positive tension flat brane, and an infinite extra dimension, we present a particular class of solutions with finite 4-dimensional Planck scale and no naked singularity. A ``self-tuning'' mechanism for relaxing the cosmological constant on the brane, without a drastic fine tuning of parameters, is discussed in this context. Our solutions are distinct from the standard self-tuning solutions discussed in the context…
We consider the well-known solution of the Heterotic Superstring effective action to zeroth order in $α'$ that describes the intersection of a fundamental string with momentum and a solitonic 5-brane and which gives a 3-charge, static, extremal, supersymmetric black hole in 5 dimensions upon dimensional reduction on $\mathrm{T}^{5}$. We compute explicitly the first-order in $α'$ corrections to this solution, including $\mathrm{SU}(2)$ Yang-Mills fields which can be used to cancel some of these corrections and we study the main properties of this $α'$-corrected solution: supersymmetry, values o…
We review work done over the last years on the macroscopic and microscopic entropy of supersymmetric black holes in fourdimensional N=2 supergravity and in N=2 compactifications of string theory and M-theory. Particular emphasis is put on the crucial role of higher curvature terms and of modifications of the area law in obtaining agreement between the macroscopic entropy, which is a geometric property of black hole solutions and the microscopic entropy, which is computed by state counting in Calabi-Yau compactifications of string or M-theory. We also discuss invariance properties of the entrop…
We study thermodynamic geometry of certain black holes and black branes with and without generalized uncertainty principle or stringy $ α^{\prime} $-corrections to the entropy. From this perspective, we analyze Ruppenier geometry of Reissner-Nordström black holes and show that it is well defined and corresponds to a non-interacting statistical system. We investigate that the Weinhold geometry of dilatonic black holes is regular everywhere and that of large mass Reissner-Nordström black holes in the Poincaré patch of $ AdS_4 $ contains certain narrow range of thermodynamically unstable regions …
We study extremal 5- and 4-dimensional black hole solutions of the Heterotic Superstring effective action at first order in $α'$ with, respectively, 3 and 4 charges of arbitrary signs. For a particular choice of the relative signs of these charges the solutions are supersymmetric, but other signs give rise to non-supersymmetric extremal black holes. Although at zeroth order all these solutions are formally identical, we show that the $α'$ corrections are drastically different depending on how we break supersymmetry. We provide fully analytic $\mathcal{O}(α')$ solutions and we compute their cha…
