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 the standard embedding. We explore the implications of these corrections for breaking no-scale structure.
The moduli of N=1 compactifications of IIB string theory can be stabilized by a combination of fluxes (which freeze complex structure moduli and the dilaton) and nonperturbative superpotentials (which freeze Kahler moduli), typically leading to supersymmetric AdS vacua. We show that stringy corrections to the Kahler potential qualitatively alter the structure of the effective scalar potential even at large volume, and can give rise to non-supersymmetric vacua including metastable de Sitter spacetimes. Our results suggest an approach to solving the cosmological constant problem, so that the sca…
The Pfaffian-Grassmannian correspondence relates certain pairs of derived equivalent non-birational Calabi-Yau 3-folds. Given such a pair, I construct a set of derived equivalences corresponding to mutations of an exceptional collection on the relevant Grassmannian, and give a mirror symmetry interpretation, following a physical analysis of Eager, Hori, Knapp, and Romo.
We study stringy fluctuations as a source for corrections to the Wilson loop as obtained from the superstrings on (adS_5 x S^5)/ N=4 SYM correspondence. We give a formal expression in terms of determinants of two dimensional operators for the leading order correction.
We consider string theory corrections to 4D black holes which solve the 5D vacuum Einstein equations. We find that the corrections vanish only for the extremal electric solution. We also show that for the non-extremal electric black hole the mass corrections are related to the charge corrections. The implications to string states counting and the correspondence principle for black holes and strings are discussed.
We study the stringy instanton partition function of four dimensional ${\cal N}=2$ $U(N)$ supersymmetric gauge theory which was obtained by Bonelli et al in 2013. In type IIB string theory on $\mathbb{C}^2\times T^*\mathbb{P}^1\times \mathbb{C}$, the stringy $U(N)$ instantons of charge $k$ are described by $k$ D1-branes wrapping around the $\mathbb{P}^1$ bound to $N$ D5-branes on $\mathbb{C}^2\times \mathbb{P}^1$. The KK corrections induced by compactification of the $\mathbb{P}^1$ give the stringy corrections. We find a relation between the stringy instanton partition function whose quantum s…
We discuss a string model where a conformal four-dimensional N=2 gauge theory receives corrections to its gauge kinetic functions from "stringy" instantons. These contributions are explicitly evaluated by exploiting the localization properties of the integral over the stringy instanton moduli space. The model we consider corresponds to a setup with D7/D3-branes in type I' theory compactified on T4/Z2 x T2, and possesses a perturbatively computable heterotic dual. In the heteoric side the corrections to the quadratic gauge couplings are provided by a 1-loop threshold computation and, under the …
We study the leading $α^\prime$ corrections to the entropy of certain black holes with AdS$_5\times S^5$ asymptotics. We find that, in the supersymmetric limit, the entropy does not receive $α^\prime$ corrections. This result strengthens recent calculations that match the index of $\mathcal{N}=4$ Super-Yang-Mills with the corresponding partition function in the supersymmetric limit. In the small temperature regime, we find that the entropy corrections are concordant with the weak gravity conjecture.
We consider one of the simplest time-dependent backgrounds in M-theory, describing the shrinking away of the M-theory dimension with the other spatial dimensions static. As the M-theory dimension becomes small, the situation becomes well-described by string theory in a singular cosmological background where the string coupling tends to zero but the $α'$-corrections become large, near the cosmic singularity. We compute these $α'$-corrections, both for the background and for linearized perturbations, in heterotic string theory, and show they may be reproduced by a map from eleven-dimensional M-t…
In this paper we explicitly obtain the leading corrections to the SU(N) N=2 prepotential due to stringy instantons both in flat space-time and in the presence of a non-trivial graviphoton background field. We show that the stringy corrections to the prepotential are expressible in terms of the elementary symmetric polynomials. For N>2 the theory is not conformal; we discuss the introduction of an explicit dependence on the string scale α' in the low-energy effective action through the stringy non-perturbative sector.
Using instanton effects, we discuss the problem of fermion mass hierarchies in an MSSM-like Type IIA orientifolded model with U(3)xSp(1)xU(1)xU(1) gauge symmetry obtained from intersecting D6-branes. In the corresponding four-stack quiver, the different scales of the generated superpotential couplings offer a partial solution to fermion mass hierarchies. Using the known data with neutrino masses m_{v_τ}\lesssim 2 eV, we give the magnitudes of the relevant scales.
We analyze the effects of zeta-function regularization on the evaluation of quantum corrections to spinning strings. Previously, this method was applied in the sl(2) subsector and yielded agreement to third order in perturbation theory with the quantum string Bethe ansatz. In this note we discuss related sums and compare zeta-function regularization against exact evaluation of the sums, thereby showing that the zeta-function regularized expression misses out perturbative as well as non-perturbative terms. In particular, this may imply corrections to the proposed quantum string Bethe equations.…
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…
We consider black holes in anti-de Sitter space AdS_{p+2} (p = 2,3,5), which have hyperbolic, flat or spherical event horizons. The $O(α'^3)$ corrections (or the leading corrections in powers of the eleven-dimensional Planck length) to the black hole metrics are computed for the various topologies and dimensions. We investigate the consequences of the stringy or M-theory corrections for the black hole thermodynamics. In particular, we show the emergence of a stable branch of small spherical black holes. We obtain the corrected Hawking-Page transition temperature for black holes with spherical …
In [1] we gave a precise holographic calculation of chaos at the scrambling time scale. We studied the influence of a small perturbation, long in the past, on a two-sided correlation function in the thermofield double state. A similar analysis applies to squared commutators and other out-of-time-order one-sided correlators [2-4]. The essential bulk physics is a high energy scattering problem near the horizon of an AdS black hole. The above papers used Einstein gravity to study this problem; in the present paper we consider stringy and Planckian corrections. Elastic stringy corrections play an …
In this paper we examine the stability of non-supersymmetric attractors in type IIA supergravity compactified on a Calabi-Yau manifold, in the presence of sub-leading corrections to the N=$ pre-potential. We study black hole configurations carrying D0-D6 and D0-D4 charges. We consider the O(1) corrections to the pre-potential given by the Euler number of the Calabi-Yau manifold. We argue that such corrections in general can not lift the zero modes for the D0-D6 attractors. However, for the attractors carrying the D0-D4 charges, they affect the zero modes in the vector multiplet sector. We show…
By studying string loop corrections to superpotential of type II strings compactified on Calabi-Yau threefolds we find a quantum stringy test and a confirmation of a recent proposal of Strominger on the fate of the conifold singularity. We also propose a connection between the spectrum of Bogomolnyi saturated solitons and one-loop string partition function of $N=2$ topological strings.
We investigate the combined effect of fluxes and higher-order curvature corrections, in the form of the Gauss-Bonnet term, on the existence of de Sitter vacua in a heterotic string inspired framework, compactified on spheres and tori. We first gain some intuition on the effects of these corrections by studying a perturbative expansion in the small Gauss-Bonnet coupling. Then, for choices of potential closer to the string theory predictions, we show that the inclusion of quadratic curvature corrections actually reduces the parametric likelihood of de Sitter solutions.
We determine one-loop string corrections to Kahler potentials in type IIB orientifold compactifications with either N=1 or N=2 supersymmetry, including D-brane moduli, by evaluating string scattering amplitudes.
String theory imposes modifications to Einstein's equations of classical general relativity. Consequently, we calculate the additional corrections to the classical tests: the perihelion precession of Mercury, the deflection of light rays by the sun, and the gravitational redshift which should be present if these modified equations hold. In each case, we determine --- quite consistently with expectations --- that the stringy effects are much too small to be measured.
Supergravity analysis suggests that the effect of fluxes in string theory compactifications is to gauge isometries of the scalar manifold. However, isometries are generically broken by brane instanton effects. Here we demonstrate how fluxes protect exactly those isometries from quantum corrections which are gauged according to the classical supergravity analysis. We also argue that all other isometries are generically broken.
Using D3/D(-1) brane set-up in type IIB string theory we introduce gauge-stringy instantons in N=2 U(N) supersymmetry theories with one matter multiplet in symmetric representation. In addition to the gauge and stringy moduli there exist extra zero modes that we refer to as "gauge-stringy" moduli. We show that the measure of the moduli space in this model becomes dimensionless for arbitary N when the gauge instanton charge k_g is equal to the stringy instanton charge k_s. This property of gauge-stringy instantons leads to having equal contributions from all instanton charges k_s=k_g=k in the e…
Non-local (alpha prime) corrections to Schwarzschild black holes are shown to invalidate the thermodynamical interpretation of black holes. In particular, the canonical and Bekenstein-Hawking temperatures are not equal. The particle number density of fields quantized in the (alpha prime modified) black hole background is no longer thermal. In the non-perturbative region (alpha prime going to infinity or mass going to zero), an analytic continuation to the number density is shown to vanish exponentially.
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…
Seiberg-Witten theory can be embedded in F-theory using D3 branes probing an orientifold geometry. The non-perturbative corrections in the orientifold picture map directly to the instanton corrections in the corresponding gauge theory that convert the classical moduli space to the quantum one. In this short review we argue that the recently proposed class of conformal Gaiotto models may also be embedded in F-theory. The F-theory constructions help us not only to understand the Gaiotto dualities but also to extend to the non-conformal cases with and without cascading behaviors. For the conforma…
Perturbative N=2 non-renormalization theorem states that there is no perturbative correction to the Kahler potential \int d^4θK(Φ,\barΦ). We prove this statement by using the N=1 supergraph techniques. We consider the N=2 supersymmetric U(1) gauge theory which possesses general prepotential F(Ψ).
We study the vacua of $4d$ heterotic toroidal orbifolds using effective theories consisting of an overall Kähler modulus, the dilaton, and non-perturbative corrections to both the superpotential and Kähler potential that respect modular invariance. We prove three de Sitter no-go theorems for several classes of vacua and thereby substantiate and extend previous conjectures. Additionally, we provide evidence that extrema of the scalar potential can occur inside the PSL$(2,\mathbb{Z})$ fundamental domain of the Kähler modulus, in contradiction of a separate conjecture. We also illustrate a loopho…
We study the effects of $ α'$ corrections to the Kähler potential on volume stabilisation and racetrack inflation. In a region where classical supergravity analysis is justified, stringy corrections can nevertheless be relevant for correctly analyzing moduli stabilisation and the onset of inflation.
Supersymmetric localization has lead to remarkable progress in computing quantum corrections to BPS black hole entropy. The program has been successful especially for computing perturbative corrections to the Bekenstein-Hawking area formula. In this work, we consider non-perturbative corrections related to polar states in the Rademacher expansion, which describes the entropy in the microcanonical ensemble. We propose that these non-perturbative effects can be identified with a new family of saddles in the localization of the quantum entropy path integral. We argue that these saddles, which are…
There has been considerable recent interest in holographic complexity. The two leading conjectures on this subject hold that the quantum complexity of the boundary thermofield double state should be dual to either the volume of the Einstein-Rosen bridge connecting the two sides (CV conjecture) or to the action of the Wheeler-de-Witt patch of the bulk spacetime (CA conjecture). Although these conjectures are frequently studied in the context of pure Einstein gravity, from the perspective of string theory it is also natural to consider models of gravity in which general relativity is perturbed b…
It is well known that non-perturbative $α'$ corrections to the $SL(2,\IR)/U(1)$ cigar geometry are described via a condensation of a Sine-Liouville operator that schematically can be written as $W^{+}+W^{-}$, where $W^{\pm}$ describe a string with winding number $\pm 1$. This condensation leads to interesting effects in the cigar geometry that take place already at the classical level in string theory. Condensation of the analytically continued Sine-Liouville operator in the Lorentzian $SL(2,\IR)/U(1)$ black hole is problematic. Here, we propose that in the black hole case, the non-perturbativ…
In low-energy effective string theory, $α'$ corrections involve the coupling of the dilaton field to Gauss-Bonnet term. We assume that the dilaton potential is fine tuned so that the dilaton field may oscillate rapidly for a while around the minimum of its potential but the inflation background is not affected. By numerical method, we find that if the dilaton starts to oscillate at the time of about $\sim 60$ e-folds before the end of inflation, $α^\prime$ correction may bring unusual oscillations to the inflationary gravitational wave spectrum, which might be measurably imprinted in the CMB B…
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 present a concrete and consistent procedure to generate one kind of non-perturbative superpotential, including the gaugino condensation corrections and poly-instanton corrections, in type IIB orientifold compactification with four Kahler Moduli. Then we use this kind of superpotential as well as the alphaprime-corrections to Kahler potential to fix all of the four Kahler moduli on a general Calabi-Yau manifold with typical K3-fibred volume form. In our construction, the considered Calabi-Yau threefolds are K3-fibred and admit at least one del Pezzo surface and one W-surface. Searching throu…
We consider the finite temperature phase diagram of holographic QCD in the Veneziano limit (Nc large, Nf large with xf=Nf/Nc fixed) and calculate one string-loop corrections to the free energy in certain approximations. Such corrections, especially due to the pion modes are unsuppressed in the Veneziano limit. We find that under some extra assumptions the first order transition following from classical gravity solutions can become second order. If stringy asymptotics are of a special form and there are residual interactions it may even become of third order. Operationally these computations im…
Recently, it has been shown that if we consider the higher derivative correction, the viscosity bound conjectured to be $η/s=1/4π$ is violated and so is the causality. In this paper, we consider medium effect and the higher derivative correction simultaneously by adding charge and Gauss-Bonnet terms. We find that the viscosity bound violation is not changed by the charge. However, we find that two effects together create another instability for large momentum regime. We argue the presence of tachyonic modes and show it numerically. The stability of the black brane requires the Gauss-Bonnet cou…
We confirm the leading $α'^3$ correction to the 4d, $\mathcal N = 1$ Kähler potential of type IIB orientifold compactifications, proportional to the Euler characteristic of the Calabi-Yau threefold (BBHL correction). We present the explicit solution for the $α'^3$-modified internal background metric in terms of the non-harmonic part of the third Chern form of the leading order Calabi-Yau manifold. The corrected internal manifold is almost Calabi-Yau and admits an $SU(3)$ structure with non-vanishing torsion. We also find that the full ten-dimensional Einstein frame background metric is multipl…
The effects of extra space-time dimensions on the Wilsonian effective Kähler potential and the perturbative one loop effective Kähler potential are determined within the framework of an Abelian gauge theory with N=2 supersymmetric field content. The relation between the Kähler metric and the effective gauge couplings which leads to the absence of radiative corrections to the Kähler potential is expressed as a function of the radius of compactification of a fifth dimension. In general, the quantum corrections to the low energy Kähler potential are shown to grow with this radius reflecting the u…
We work out the exact in string coupling and perturbatively exact in α' result for the vector multiplet moduli Kähler potential in a specific N=2 compactification of F-theory. The well-known correction cubic in α' is absent, but there is a rich structure of corrections at all even orders in α'. Moreover, each of these orders independently displays an SL(2,Z) invariant set of corrections in the string coupling. This generalizes earlier findings to the case of a non-trivial elliptic fibration. Our results pave the way for the analysis of quantum corrections in the more complicated N=1 context, a…
In d>4 dimensions, one can argue for the existence of small black rings using a scaling argument. We apply the same scaling argument to the d=4 case and demonstrate that it fails to say anything about the existence of d=4 small black rings, because stringy corrections get out of control. General relativity theorems say that there does not exist a black hole with toroidal topology for d=4, but we interpret this as saying that, for d=4 small black rings, stringy corrections are crucial which invalidate the assumptions those theorems are based on.
In this work we analyze F-theory and Type IIB orientifold compactifications to study $α'$-corrections to the four-dimensional, $\mathcal{N} = 1$ effective actions. In particular, we obtain corrections to the Kählermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the $G^ 2 R^3$ and $(\nabla G)^2R^2$-sector in eleven-dimensions relevant in Calabi--Yau fourfold reductions. We suggest that the three-dimensional, $\mathcal{N}=2$ Kähler coordinates may be expressed as topol…
The non-perturbative dynamics of quantum field theories is studied using theoretical tools inspired by string formalism. Two main lines are developed: the analysis of stringy instantons in a class of four-dimensional N=2 gauge theories and the holographic study of the minimal model for a strongly coupled unbalanced superconductor. The field theory instanton calculus admits a natural and efficient description in terms of D-brane models. In addition, the string viewpoint offers the possibility of generalizing the ordinary instanton configurations. Even though such generalized, or stringy, instan…
We consider hairy black hole solutions of Einstein-Yang-Mills-Dilaton theory, coupled to a Gauss-Bonnet curvature term, and we study their stability under small, spacetime-dependent perturbations. We demonstrate that the stringy corrections do not remove the sphaleronic instabilities of the coloured black holes with the number of unstable modes being equal to the number of nodes of the background gauge function. In the gravitational sector, and in the limit of an infinitely large horizon, the coloured black holes are also found to be unstable. Similar behaviour is exhibited by the magnetically…
We extend and generalise the string corrections to the EM memory to the Type I superstring including spin effects. Very much as in the simpler bosonic string context, the relevant corrections are non-perturbative in $α'$, slowly decaying (as $1/R$) at large distances and modulated in retarded time $u=t-R$. For spin $N$ states in the first Regge trajectory they entail a sequence of $N$ derivatives wrt $u$ on the `parent' $N=0$ amplitude. We also briefly discuss how to include loop effects, that broaden and shift the string resonances, and how to modify our analysis for macroscopic semi-classica…
We perform a Kaluza-Klein reduction of eleven-dimensional supergravity on a Calabi-Yau fourfold including terms quartic and cubic in the Riemann curvature and determine the induced corrections to the three-dimensional N=2 effective action. We focus on the effective Einstein-Hilbert term and the kinetic terms for vectors. Dualizing the vectors into scalars, we derive the resulting Kahler potential and complex coordinates. The classical expressions for the Kahler coordinates are non-trivially modified, while the functional form of the Kahler potential is shown to be uncorrected. For elliptically…
We study cosmological solutions to the low-energy effective action of heterotic string theory including possible leading order $α'$ corrections and a potential for the dilaton. We consider the possibility that including such stringy corrections can resolve the initial cosmological singularity. Since the exact form of these corrections is not known the higher-derivative terms are constructed so that they vanish when the metric is de Sitter spacetime. The constructed terms are compatible with known restrictions from scattering amplitude and string worldsheet beta-function calculations. Analytic …
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…
In N=2 superconformal field theories the Kahler potential is known to be tree level exact. The beta-deformation of N=4 SU(N) SYM reduces the amount of supersymmetry to N=1, allowing for non-trivial, superconformal loop corrections to the Kahler potential. We analyse the two-loop corrections on the Coulomb branch for a complex deformation. For an arbitrary chiral field in the Cartan subalgebra we reduce the problem of computing the two-loop Kahler potential to that of diagonalising the mass matrix, we then present the result in a manifestly superconformal form. The mass matrix diagonalisation i…
In the framework of special Kahler geometry we consider the supergravity-matter system which emerges on a K3-fibered Calabi-Yau manifold. By applying the rigid limit procedure in the vicinity of a conifold singularity we compute the Kahler potential of the scalars and the kinetic matrix of the vectors to first order in the gravitational coupling.
