We provide arguments for the existence of novel hereinafter called poly-instanton corrections to holomorphic couplings in four-dimensional N=1 supersymmetric string compactifications. After refining quantitatively the D-brane instanton calculus for corrections to the gauge kinetic function, we explicitly apply it to the Type I toroidal orbifold defined in arXiv:0710.3080 and compare the results to the proposed heterotic S-dual model. This leads us to the intriguing conclusion that N=1 string vacua feature a power tower like proliferation of instanton corrections.
In this paper, we present a series of supersymmetric models exhibiting an entirely new vacuum structure: towers of metastable vacua with higher and higher energies. As the number of vacua grows towards infinity, the energy of the highest vacuum remains fixed while the energy of the true ground state tends towards zero. We study the instanton-induced tunneling dynamics associated with such vacuum towers, and find that many distinct decay patterns along the tower are possible: these include not only regions of vacua experiencing direct collapses and/or tumbling cascades, but also other regions o…
We investigate membrane instanton effects in type IIA strings compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet. In the absence of additional fivebrane instantons, the quaternionic geometry of this hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons, and find perfect agreement with the string theory prediction. In the context of flux compactifications we discuss how membrane instantons contribute to the scalar potential and th…
Recently discovered models of ghost-free massive gravity and bigravity are characterized by a non-trivial potential that gives rise to a rich vacuum structure. We review maximally symmetric vacua of the de Rham-Gabadadze-Tolley (dRGT) massive gravity and of the Hassan-Rosen (HR) bigravity, and discuss their perturbative stability. In particular, we discuss perturbations about self-accelerating vacua in HR bigravity, and argue that, analogously to what was found in the case of dRGT gravity, some of them contain strongly coupled modes. We then show that it is impossible to construct regular inst…
We construct a generalization of Witten's Kaluza-Klein instanton, where a higher-dimensional sphere (rather than a circle as in Witten's instanton) collapses to zero size and the geometry terminates at a bubble of nothing, in a low energy effective theory of M theory. We use the solution to exhibit instability of non-supersymmetric AdS_5 vacua in M Theory compactified on positive Kaehler-Einstein spaces, providing a further evidence for the recent conjecture that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable.
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 some aspects of D-instantons in intersecting D-brane models. In particular, we present applications of the recently proposed instanton calculus to computations of charged matter superpotential couplings and corrections to the gauge kinetic function in the low energy effective action of type IIA orientifolds. As an interesting byway, we also discuss how one-loop corrections to the gauge kinetic function can be deduced from gauge threshold corrections in the type IIA setting.
We consider instanton contributions to chiral correlators, such as <0| Tr λ^2 (x) Tr λ^2(x') |0>, in N=1 supersymmetric Yang-Mills theory with either light adjoint or fundamental matter. Within the former model, extraction of the gluino condensate from a connected 1-instanton diagram, evaluated at strong coupling, can be contrasted with expectations from the Seiberg-Witten solution perturbed to an N=1 vacuum. We observe a numerical discrepancy, coinciding with that observed previously in N=1 SQCD. Moreover, since knowledge of the vacuum structure is complete for softly broken N=2 Yang-Mills, t…
Instantons and their quantisation in pure Yang-Mills theory formulated in the background of de Sitter spacetime represented by spatially-closed ($k = 1$) Friedmann-Robertson-Walker metric are discussed. As for the classical treatment of the instanton physics, first, explicit instanton solutions are found and next, quantities like Pontryagin index and the semiclassical approximation to the inter-vacua tunnelling amplitude are evaluated. The Atiyah-Patodi-Singer index theorem is checked as well by constructing explicitly the normalizable fermion zero modes in this de Sitter spacetime instanton b…
We show that for the triple well potential with non-equivalent vacua, instantons generate for the low lying energy states a singlet and a doublet of states rather than a triplet of equal energy spacing. Our energy splitting formulae are also confirmed numerically. This splitting property is due to the presence of non-equivalent vacua. A comment on its generality to multi-well is presented.
In supersymmetric QCD with SU(N_c) gauge group and N_f flavors, it is known that instantons generate a superpotential if N_f=N_c-1 and deform the moduli space of vacua if N_f=N_c. But the role of instantons has been unclear for N_f>N_c. In this paper, we demonstrate that for N_f>N_c, on the moduli space of vacua, instantons generate a more subtle chiral operator containing (for example) non-derivative interactions of 2(N_f-N_c)+4 fermions. Upon giving masses to some flavors, one can integrate out some fermions and recover the standard results for N_f=N_c and N_f=N_c-1. For N_f=N_c, our analysi…
We construct a large class of SU(5) orientifold vacua with tadpole cancellation both for the standard and the flipped case. We give a general analysis of superpotential couplings up to quartic order in orientifold vacua and identify the properties of needed Yukawa couplings as well as the baryon number violating couplings. We point out that successful generation of the perturbatively forbidden Yukawa couplings entails a generically disastrous rate for proton decay from an associated quartic term in the superpotential, generated from the same instanton effects. We search for the appropriate ins…
We investigate the instanton solution between the degenerate vacua in curved space. We show that there exist $O(4)$-symmetric solutions not only in de Sitter but also in both flat and anti-de Sitter space. The geometry of the new type of solutions is finite and preserves the $Z_2$ symmetry. The nontrivial solution corresponding to the tunneling is possible only if gravity is taken into account. The numerical solutions as well as the analytic computations using the thin-wall approximation are presented. We expect that these solutions do not have any negative mode as in the instanton solution.
We systematically investigate instanton corrections from wrapped Euclidean D-branes to the matter field superpotential of various classes of N=1 supersymmetric D-brane models in four dimensions. Both gauge invariance and the counting of fermionic zero modes provide strong constraints on the allowed non-perturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a one-loop vacuum diagram. For concreteness we focus on E2-instanton effects in Type IIA vacua with in…
We construct worldsheet descriptions of heterotic flux vacua as the IR limits of N=2 gauge theories. Spacetime torsion is incorporated via a 2d Green-Schwarz mechanism in which a doublet of axions cancels a one-loop gauge anomaly. Manifest (0,2) supersymmetry and the compactness of the gauge theory instanton moduli space suggest that these models, which include Fu-Yau models, are stable against worldsheet instanton effects, implying that they, like Calabi-Yaus, may be smoothly extended to solutions of the exact beta functions. Since Fu-Yau compactifications are dual to KST-type flux compactifi…
We study the influence of four-form fluxes on the stabilization of the Kahler moduli in M-theory compactified on a Calabi-Yau four-fold. We find that, under certain non-degeneracy condition on the flux, M5-instantons of a new topological type generate a superpotential. The existence of such an instanton restricts possible four-folds for which the stabilization by this mechanism is expected. These topological constraints on the background are different from the previously known constraints, derived from the flux-free analysis of the nonperturbative effects.
We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpr…
We argue that theories with multiple axions generically contain a large number of vacua that can account for the smallness of the cosmological constant. In a theory with N axions, the dominant instantons with charges Q determine the discrete symmetry of vacua. Subleading instantons break the leading periodicity and lift the vacuum degeneracy. For generic integer charges the number of distinct vacua is given by |det(Q)|~exp(N). Our construction motivates the existence of a landscape with a vast number of vacua in a large class of four-dimensional effective theories.
By analyzing qualitative aspects of NS5-brane instanton corrections, we determine the topology of the hypermultiplet moduli space M_H in Calabi-Yau compactifications of type II string theories at fixed value of the dilaton and of the Calabi-Yau metric. Specifically, we show that for fivebrane instanton couplings to be well-defined, translations along the intermediate Jacobian must induce non-trivial shifts of the Neveu-Schwarz axion which had thus far been overlooked. As a result, the Neveu-Schwarz axion parametrizes the fiber of a circle bundle, isomorphic to the one in which the fivebrane pa…
We compute one-loop threshold corrections to R^4 terms in N= 5,6 supergravity vacua of Type II superstrings. We then discuss non-perturbative corrections generated by asymmetric D-brane instantons. Finally we derive generating functions for MHV amplitudes at tree level in N = 5, 6 supergravities.
M(atrix) theory in PP-wave background possesses a discrete set of classical vacua, all of which preserves 16 supersymmetry and interpretable as collection of giant gravitons. We find Euclidean instanton solutions that interpolate between them, and analyze their properties. Supersymmetry prevents direct mixing between different vacua but still allows effect of instanton to show up in higher order effective interactions, such as analog of v^4 interaction of flat space effective theory. An explicit construction of zero modes is performed, and Goldstone zero modes, bosonic and fermionic, are ident…
We extend a recent scenario of Kachru, Kallosh, Linde and Trivedi to fix the string moduli fields by using a combination of fluxes and non-perturbative superpotentials, leading to de Sitter vacua. In our scenario the non-perturbative superpotential is taken to be the N=1^* superpotential for an SU(N) theory, originally computed by Dorey and recently rederived using the techniques of Dijkgraaf-Vafa. The fact that this superpotential includes the full instanton contribution gives rise to the existence of a large number of minima, increasing with N. In the absence of supersymmetry breaking these …
$QCD_2$ with fermions in the adjoint representation is invariant under $SU(N)/Z_N$ and thereby is endowed with a non-trivial vacuum structure (k-sectors). The static potential between adjoint charges, in the limit of infinite mass, can be therefore obtained by computing Wilson loops in the pure Yang-Mills theory with the same non-trivial structure. When the (Euclidean) space-time is compactified on a sphere $S^2$, Wilson loops can be exactly expressed in terms of an infinite series of topological excitations (instantons). The presence of k-sectors modifies the energy spectrum of the theory and…
Two-dimensional SU(N) Yang-Mills theory is endowed with a non-trivial vacuum structure (k-sectors). The presence of k-sectors modifies the energy spectrum of the theory and its instanton content, the (Euclidean) space-time being compactified on a sphere. For the exact solution, in the limit in which the sphere is decompactified, a k-sector can be mimicked by the presence of k-fundamental charges at infinity, according to a Witten's suggestion. However, this property neither holds before decompactification nor for the genuine perturbative solution which corresponds to the zero-instanton contrib…
Flux Vacua Near the Boundary of Large Complex Structure
Harish-Chandra Research Institute（哈里什-昌德拉研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼亚分部）；Leinweber Institute for Theoretical Physics, Randall Laboratory of Physics, University of Michigan（密歇根大学莱恩韦伯理论物理研究所兰德尔物理实验室）；New York University Abu Dhabi（纽约大学阿布扎比分校）
The moduli space of spiked instantons that arises in the context of the BPS/CFT correspondence is realised as the moduli space of classical vacua, i.e. low-energy open string field configurations, of a certain stack of intersecting D1-branes and D5-branes in Type IIB string theory. The presence of a constant B-field induces an interesting dynamics involving the tachyon condensation.
One of the central problems of string-phenomenology is to find stable vacua in the four dimensional effective theories which result from compactification. We present an algorithmic method to find all of the vacua of any given string-phenomenological system in a huge class. In particular, this paper reviews and then extends hep-th/0606122 to include various non-perturbative effects. These include gaugino condensation and instantonic contributions to the superpotential.
We review the structure $D=6, N=1$ string vacua with emphasis on the different connections due to T-dualities and S-dualities. The topics discussed include: Anomaly cancellation; K3 and orbifold $D=6, N=1$ heterotic compactifications; T-dualities between $E_8\times E_8$ and $Spin(32)/Z_2$ heterotic vacua; non-perturbative heterotic vacua and small instantons; N=2 Type-II/Heterotic duality in D=4 ; F-theory/heterotic duality in D=6; and heterotic/heterotic duality in six and four dimensions.
We study the condensation of localized closed string tachyons on AdS orbifolds both from the bulk and boundary theory viewpoints. We first extend the known results for AdS_5/Z_k to AdS_3/Z_k case, and we proposed that the AdS_3/Z_k decays into AdS_3/Z_k' with k' < k. From the bulk viewpoint, we obtain a time-dependent gravity solution describing the decay of AdS orbifold numerically. From the dual gauge theory viewpoint, we calculated the Casimir energies of gauge theory vacua and it is found that their values are exactly the same as the masses of dual geometries, even though they are in diffe…
Structure group SU(4) gauge vacua of both weakly and strongly coupled heterotic superstring theory compactified on torus-fibered Calabi-Yau threefolds Z with Z_2 x Z_2 fundamental group are presented. This is accomplished by constructing invariant, stable, holomorphic rank four vector bundles on the simply connected cover of Z. Such bundles can descend either to Hermite-Yang-Mills instantons on Z or to twisted gauge fields satisfying the Hermite-Yang-Mills equation corrected by a non-trivial flat B-field. It is shown that large families of such instantons satisfy the constraints imposed by par…
We study general aspects of NS5-brane instantons in relation to the stabilization of the volume modulus in Calabi-Yau compactifications of type II strings with fluxes, and their orientifold versions. These instantons correct the Kahler potential and generically yield significant contributions to the scalar potential at intermediate values of string coupling constant and volume. Under suitable conditions they yield uplifting terms that allow for meta--stable de Sitter vacua.
Multicenter supergravity solutions corresponding to Higgs phases of supersymmetric Yang-Mills theories are considered. For NS5 branes we identify three cases where there is a description in terms of exact conformal field theories. Other supergravity solutions, such as D3-branes with angular momentum, are understood as special limits of multicenter ones. Within our context we also consider 4-dim gravitational multi-instantons.
We study tunneling between vacua in multi-dimensional field spaces. Working in the strict thin wall approximation, we find that the conventional instantons for false vacuum decay develop a new vanishing eigenvalue in their fluctuation determinant, arising from decorations of the nucleating bubble wall with small spots of the additional vacua. Naively, this would suggest that the presence of additional vacua in field space leads to a substantial enhancement of the nucleation rate. However, we argue that this potential enhancement is regulated away by the finite thickness of physical bubble wall…
We analyze three aspects of N=1 heterotic string compactifications on elliptically fibered Calabi-Yau threefolds: stability of vector bundles, five-brane instanton transitions and chiral matter. First we show that relative Fourier-Mukai transformation preserves absolute stability. This is relevant for vector bundles whose spectral cover is reducible. Then we derive an explicit formula for the number of moduli which occur in (vertical) five-brane instanton transitions provided a certain vanishing argument applies. Such transitions increase the holonomy of the heterotic vector bundle and cause g…
We investigate membrane and fivebrane instanton effects in type IIA string theory compactified on rigid Calabi-Yau manifolds. These effects contribute to the low-energy effective action of the universal hypermultiplet, in four dimensional spacetime. To compute the nonperturbative effects due to the fivebrane instanton to the universal hypermultiplet, an instanton calculation is performed. In the absence of fivebrane instantons, the quaternionic geometry of the hypermultiplet is determined by solutions of the three-dimensional Toda equation. We construct solutions describing membrane instantons…
The quantum symmetry of many \LG\ orbifolds appears to be broken by Yang-Mills instantons. However, isolated Yang-Mills instantons are not solutions of string theory: They must be accompanied by gauge anti-instantons, gravitational instantons, or topologically non-trivial configurations of the $H$ field. We check that the configurations permitted in string theory do in fact preserve the quantum symmetry, as a result of non-trivial cancellations between symmetry breaking effects due to the various types of instantons. These cancellations indicate new constraints on \LG\ orbifold spectra and req…
Owing to the quadratic nature of the theory, Einstein-Gauss-Bonnet gravity generically permits two distinct vacuum solutions. One solution (the "Einstein" vacuum) has a well defined limit as the Gauss-Bonnet coupling goes to zero, whereas the other solution (the "stringy" vacuum) does not. There has been some debate regarding the stability of these vacua, most recently from Deser and Tekin who have argued that the corresponding black hole solutions have positive mass and as such both vacua are stable. Whilst the statement about the mass is correct, we argue that the stringy vacuum is still per…
We study ${\cal F}^4$-threshold corrections in an eight dimensional S-dual pair of string theories, as a prototype of dual string vacua with sixteen supercharges. We show that the orbifold CFT description of D-string instantons gives rise to a perturbative expansion similar to the one appearing on the fundamental string side. By an explicit calculation, using the Nambu-Goto action in the static gauge, we show that the first subleading term agrees precisely on the two sides. We then give a general argument to show that the agreement extends to all orders.
This letter discusses the orientifold projection of the quantum corrections to type IIA strings compactified on rigid Calabi-Yau threefolds. It is shown that N=2 membrane instanton effects give a holomorphic contribution to the superpotential, while the perturbative corrections enter into the Kahler potential. At the level of the scalar potential the corrections to the Kahler potential give rise to a positive energy contribution similar to adding anti-D3-branes in the KKLT scenario. This provides a natural mechanism to lift an AdS vacuum to a meta-stable dS vacuum.
A long-standing puzzle about the heterotic string has been what happens when an instanton shrinks to zero size. It is argued here that the answer at the quantum level is that an extra $SU(2)$ gauge symmetry appears that is supported in the core of the instanton. Thus in particular the quantum heterotic string has vacua with higher rank than is possible in conformal field theory. When $k$ instantons collapse at the same point, the enhanced gauge symmetry is $Sp(k)$. These results, which can be tested by comparison to Dirichlet five-branes of Type I superstrings and to the ADHM construction of i…
It is emphasized that compactified little string theories have compact moduli spaces of vacua, which globally probe compact string geometry. Compactifying various little string theories on T^3 leads to 3d theories with exact, quantum Coulomb branch given by: an arbitrary T^4 of volume M_s^2, an arbitrary K3 of volume M_s^2, and moduli spaces of G=SU(N), SO(2N), or E_{6,7,8} instantons on an arbitrary T^4 or K3 of fixed volume. Compactifying instead on a T^2 leads to 4d theories with a compact Coulomb branch base which, when combined with the exact photon gauge coupling fiber, is a compact, ell…
We compute the instanton expansions of the holomorphic couplings in the effective action of certain $\cx N=1$ supersymmetric four-dimensional open string vacua. These include the superpotential $W(ϕ)$, the gauge kinetic function $f(ϕ)$ and a series of other holomorphic couplings which are known to be related to amplitudes of topological open strings at higher world-sheet topologies. The results are in full agreement with the interpretation of the holomorphic couplings as counting functions of BPS domain walls. Similar techniques are used to compute genus one partition function for the closed t…
Heterotic strings on $R^6 \times K3$ generically appear to undergo some interesting new phase transition at that value of the string coupling for which the one of the six-dimensional gauge field kinetic energies changes sign. An exception is the $E_8 \times E_8$ string with equal instanton numbers in the two $E_8$'s, which admits a heterotic/heterotic self-duality. In this paper, we generalize the dyonic string solution of the six-dimensional heterotic string to include non-trivial gauge field configurations corresponding to self-dual Yang-Mills instantons in the four transverse dimensions. We…
In these lecture notes duality tests and instanton effects in supersymmetric vacua of string theory are discussed. A broad overview of BPS-saturated terms in the effective actions is first given. Their role in testing the consistency of duality conjectures as well as discovering the rules of instanton calculus in string theory is discussed. The example of heterotic/type-I duality is treated in detail. Thresholds of F^4 and R^4 terms are used to test the duality as well as to derive rules for calculated with D1-brane instantons. We further consider the case of R^2 couplings in N=4 ground-states…
Decay of a de Sitter vacuum may proceed through a "static" instanton, representing pair creation of critical bubbles separated by a distance comparable to the Hubble radius -- a process somewhat analogous to thermal activation in flat space. We compare this with related processes recently discussed in the literature.
We study limits of infinite distance in the moduli space of 4d $\mathcal{N} = 2$ string compactifications, in which instanton effects dominate. We first consider trajectories in the hypermultiplet moduli space of type IIB Calabi-Yau compactifications. We observe a correspondence between towers of D-brane instantons and D-brane 4d strings, such that the lighter the string the more relevant the instanton effects are. The dominant instantons modify the classical trajectory such that the lightest D-brane string becomes tensionless even faster, while the other strings are prevented to go below the …
We review how D-brane instantons can generate open string couplings of stringy hierarchy in the superpotential which violate global abelian symmetries and are therefore perturbatively forbidden. We discuss the main ingredients of this mechanism, focussing for concreteness on Euclidean $D2$-branes in Type IIA orientifold compactifications. Special emphasis is put on a careful analysis of instanton zero modes and a classification of situations leading to superpotential or higher fermionic F-terms. This includes the discussion of chiral and non-chiral instanton recombination, viewed as a multi-in…
When the gauge instantons on the N=2 string worldsheet are properly included in the sum over topologies, the breaking of SO(2,2) Lorentz symmetry in R^{2,2} is parametrized by a spacetime twistor containing the string coupling and theta angle. The resulting (tree-level) effective action for the open string is not Yang's but Leznov's cubic action for self-dual Yang-Mills in a light-cone gauge. In the closed case, Plebanski's action for self-dual gravity gets modified analogously. In contrast to the N=1 NSR string, picture-changing is not locally invertible, but produces a semi-infinite tower of…
We present a construction of domain walls in string theory. The domain walls can bridge both Minkowski and AdS string vacua. A key ingredient in the construction are novel classical Yang-Mills configurations, including instantons, which interpolate between toroidal Yang-Mills vacua. Our construction provides a concrete framework for the study of inflating metrics in string theory. In some cases, the accelerating space-time comes with a holographic description. The general form of the holographic dual is a field theory with parameters that vary over space-time.
We consider a novel scenario for modulus stabilisation in IIB string compactifications in which the Kahler moduli are stabilised by a general set-up with two kinds of non-perturbative effects: (i) standard Kahler moduli-dependent non-perturbative effects from gaugino condensation on D7-branes or E3-instantons wrapping four-cycles in the geometric regime; (ii) dilaton-dependent non-perturbative effects from gaugino condensation on space-time filling D3-branes or E(-1)-instantons at singularities. For the LARGE Volume Scenario (LVS), the new dilaton-dependent non-perturbative effects provide a p…
We discuss the four-dimensional N=1 effective approach in the study of warped type II flux compactifications with SU(3)x SU(3)-structure to AdS_4 or flat Minkowski space-time. The non-trivial warping makes it natural to use a supergravity formulation invariant under local complexified Weyl transformations. We obtain the classical superpotential from a standard argument involving domain walls and generalized calibrations and show how the resulting F-flatness and D-flatness equations exactly reproduce the full ten-dimensional supersymmetry equations. Furthermore, we consider the effect of non-pe…
The most general large N eigenvalues distribution for the one matrix model is shown to consist of tree-like structures in the complex plane. For the m=2 critical point, such a split solution describes the strong coupling phase of 2d quantum gravity (c=0 non-critical string). It is obtained by taking combinations of complex contours in the matrix integral, and the relative weight of the contours is identified with the non-perturbative theta-parameter that fixes uniquely the solution of the string equation (Painleve I). This allows to recover by instanton methods results on the non-perturbative …
As a first step toward understanding a lanscape of vacua in a theory of non-linear massive gravity, we consider a landscape of a single scalar field and study tunneling between a pair of adjacent vacua. We study the Hawking-Moss (HM) instanton that sits at a local maximum of the potential, and evaluate the dependence of the tunneling rate on the parameters of the theory. It is found that provided with the same physical HM Hubble parameter $H_{HM}$, depending on the values of parameters $α_3$ and $α_4$ in the action, the corresponding tunneling rate can be either enhanced or suppressed when com…
Supercritical string theories in D>10 dimensions with no moduli are described, generalizing the asymmetric orientifold construction of one of the authors. By taking the number of dimensions to be large and turning on fluxes, dilaton potentials are generated with nontrivial minima at arbitrarily small cosmological constant and D-dimensional string coupling, separated by a barrier from a flat-space linear dilaton region, but possibly suffering from strong coupling problems. The general issue of the decay of a de Sitter vacuum to flat space is discussed. For relatively small barriers, such decays…
Motivated by precision counting of BPS black holes, we analyze six-derivative couplings in the low energy effective action of three-dimensional string vacua with 16 supercharges. Based on perturbative computations up to two-loop, supersymmetry and duality arguments, we conjecture that the exact coefficient of the $\nabla^2(\nablaϕ)^4$ effective interaction is given by a genus-two modular integral of a Siegel theta series for the non-perturbative Narain lattice times a specific meromorphic Siegel modular form. The latter is familiar from the Dijkgraaf-Verlinde-Verlinde (DVV) conjecture on exact…
