Latex, 31 pages, no figures; v2: some typos corrected, a short discussion on standard model embedding, and references added. Final version to appear in JHEP
We study the axion in a warped heterotic background. It is shown that the axion decay constant, f_a, is sensitive to the warped mass scale of the throat. As an explicit model, we construct a novel AdS-like geometry in heterotic string theory. We demonstrate that in this background f_a is given by the mass scale of the longest throat in the compactification. The question of obtaining f_a within the required bound 10^9--10^12 GeV is reduced to the construction of a throat inside the heterotic string theory compactification with warped mass scale in the above range. This provides a natural mechanism for realising the axion in heterotic string theory.
A previously discussed clockwork mechanism within heterotic M-theory is applied to its axion landscape. We identify a unique candidate for a QCD-axion with a decay constant in the preferred "axion window" around $10^{11}\,$GeV. It is accompanied by at least one ultra-light axion that couples predominantly to hidden sector gauge groups.
In the framework of heterotic M-theory compactified on a Calabi-Yau threefold 'times' an interval, the relation between geometry and four-flux is derived {\it beyond first order}. Besides the case with general flux which cannot be described by a warped geometry one is naturally led to consider two special types of four-flux in detail. One choice shows how the M-theory relation between warped geometry and flux reproduces the analogous one of the weakly coupled heterotic string with torsion. The other one leads to a {\it quadratic} dependence of the Calabi-Yau volume with respect to the orbifold…
We study a number of realizations of axions existing in a multi-`throat' generalization of the warped throat geometry of a Randall-Sundrum slice of $AdS_5$. As argued by previous authors, the problem of generating a suitable, phenomenologically allowed Peccei-Quinn scale is simply and elegantly solved by the warping. In compactifications with two or more throats it is possible to simultaneously solve the Standard Model hierarchy problem by the Randall-Sundrum mechanism while implementing interesting warped axion models. The constructions discussed are related to holographic duals of previously…
We classify all warped product de-Sitter backgrounds in heterotic supergravity, up to two loops. We find that warped $dS_n$ backgrounds, with $n\ge 3$, are $\mathbb{R}^{1,n}\times M_{9-n}$, where $M_{9-n}$ is a $(9-n)$-dimensional Riemannian manifold. Moreover, we establish that warped $dS_2$ backgrounds are $AdS_3\times M_7$, where $M_7$ is a 7-dimensional Riemannian manifold.
A set of consistency conditions is derived for the massless sector of the D-dimensional E(8)xE(8) heterotic string. Under the solvable Lie algebra gauge these conditions are further formulated explicitly in terms of the dilatons and the axions. It is then shown that these consistency conditions which are satisfied by the solution space give way to an implicit decoupling between the coset scalar sector namely the dilatons and the axions and the gauge fields of the theory.
We propose the natural inflation from the heterotic string theory on "Swiss-Cheese" Calabi-Yau manifold with multiple $U(1)$ magnetic fluxes. Such multiple $U(1)$ magnetic fluxes stabilize the same number of the linear combination of the universal axion and Kähler axions and one of the Kähler axions is identified as the inflaton. This axion decay constant can be determined by the size of one-loop corrections to the gauge kinetic function of the hidden gauge groups, which leads effectively to the trans-Planckian axion decay constant consistent with the WMAP, Planck and/or BICEP2 data. During th…
We present a connection between two known solutions to the strong-CP problem: the standard introduction of axions and the extra-dimensional one, relying on topological arguments. Using an equivalent lower-dimensional set-up with a warped extra-dimension but without adding any new fields, it is shown that an additional light degree of freedom appears. Like an axion, it couples to the topological charge density via Fermionic loop corrections. Its decay constant is related to the geometry of the extra dimension and is suppressed by the warping scale.
We consider 1+3-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kähler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [arXiv:1109.3552]. We include first order $α'$ corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present a variety of solutions, depending on the choice of instantons, for the special case in which the SU(3) structure on $X_6$ satisfies $W_1^-=0$. The solutions preserve two real supercharges, which correspo…
We show that a KSVZ axion with a decay constant in the phenomenologically allowed range can be obtained in certain $E_8\times E_8$ heterotic string models. These models have an enhanced symmetry locus in the moduli space, and a non-universal, Kahler moduli dependent Fayet-Iliopoulos term which vanishes at this locus. Close to this locus the Fayet-Iliopoulos term is small and can lead to an axion decay constant significantly lower than the string scale. In this way, the no-go arguments of Svrcek and Witten, which are based on a universal, dilaton-dependent Fayet-Iliopoulos term, can be avoided.…
We consider heterotic strings on a warped Eguchi-Hanson space with five-brane and line bundle gauge fluxes. The heterotic string admits an exact CFT description in terms of an asymmetrically gauged SU(2)xSL(2,R) WZW model, in a specific double scaling limit in which the blow-up radius and the string scale are sent to zero simultaneously. This allows us to compute the perturbative 6D spectra for these models in two independent fashions: i) Within the supergravity approximation we employ a representation dependent index; ii) In the double scaling limit we determine all marginal vertex operators …
Some recent developments in the weakly-coupled heterotic string phenomenology are reviewed. We discuss several important issues such as dilaton/moduli stabilization, supersymmetry breaking (by hidden-sector gaugino condensation), gauge coupling unification (or the Newton's constant), the QCD axion, as well as cosmological problems involving the dilaton/moduli and the axion.
We consider a 5D extension of the DFSZ axion model that addresses both the axion quality and fermion mass hierarchy problems, and predicts flavour-dependent, off-diagonal axion-fermion couplings. The axion is part of a 5D complex scalar field charged under a U(1)$_{PQ}$ symmetry that is spontaneously broken in the bulk, and is insensitive to explicit PQ breaking on the UV boundary. Bulk Standard Model fermions interact with two Higgs doublets that can be localized on the UV boundary or propagate in the bulk to explain the fermion masses and mixings. When the Higgs doublets are localized on the…
We explore the possibility of obtaining inflation in weakly coupled heterotic string theory, where the model dependent axions are responsible for driving inflation. This model can be considered as a certain extrapolation of $m^{2}ϕ^{2}$-inflation, and is an attempt to explicitly realize the so called N-flation proposal in string theory. The instanton generated potential for the axions essentially has two parameters; a natural mass scale $M$ and the string coupling $g_{s}$. For isotropic compactifications leading to of order $\mathcal{O} (10^4)$ axions in the four dimensional spectrum we find t…
Recent models of axion monodromy inflation in string theory link the inflationary potential and the moduli stabilization potential. Realistic inflationary models require mechanisms to moderately suppress the inflaton mass with respect to the moduli stabilization scale. In this paper we explore the realization of this idea using warped throats, whose redshifted infrared region supports the inflaton mode. The inflaton potential and its monodromy arise from couplings to the fluxes supporting the throat. We provide explicit realizations of such throats in type IIB with NSNS and RR 3-form field str…
New and surprisingly simple representation is found for the heterotic string bosonic effective action in three dimensions in terms of complex potentials. The system is presented as a Kähler $σ$--model using complex symmetric $2\times 2$ matrix (matrix dilaton--axion) which depends linearly on three Ernst--type potentials and transforms under $U$--duality via matrix valued $SL(2,R)$. Two discrete automorphisms relating ten isometries of the target space (U--duality transformations) are found and used to generate the non--trivial Ehlers--Harrison sector by a map from the trivial gauge sector. Fi…
Low energy string theory predicts the existence of an axion field which can lead to cosmic birefringence. We solve the electromagnetic wave equations in the presence of such an axion and a dilaton field in order to determine their effect on the polarization of light. We find that the presence of dilaton field leads to a nontrivial modification of the final result. We comment on the possibility of discovering such an effect by observations of radio wave polarizations from distant radio galaxies and quasars. We have also determined the limits on the string theory parameters that are imposed by t…
We give necessary conditions for the existence of perturbative heterotic and common sector type II string warped compactifications preserving four and eight supersymmetries to four spacetime dimensions, respectively. In particular, we find that the only compactifications of heterotic string with the spin connection embedded in the gauge connection and type II strings are those on Calabi-Yau manifolds with constant dilaton. We obtain similar results for compactifications to six and to two dimensions.
We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with $n\not=3$. Moreover the warp factor of AdS$_3$ backgrounds is constant, the geometry is a product $AdS_3\times M^7$ and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of $M^7$ has been specified in all cases. For 2 supersymmetries, it has been found that $M^7$ admits a suitably restricted $G_2$ structure. For 4 supersymmetries, $M^7$ has …
We interpret D-strings at the bottom of the warped deformed conifold as axionic strings in the dual cascading SU(N+M) x SU(N) gauge theory. The axion is a massless pseudo-scalar glueball which we find in the supergravity fluctuation spectrum and interpret as the Goldstone boson of spontaneously broken U(1) baryon number symmetry. The existence of this massless glueball, anticipated in hep-th/0101013, supports the idea that the cascading gauge theory is on the baryonic branch, i.e. the U(1)_B global symmetry is broken by expectation values of baryonic operators. We also find a massless scalar g…
We consider the class of effective supergravity theories from the weakly coupled heterotic string in which local supersymmetry is broken by gaugino condensation in a hidden sector, with dilaton stabilization achieved through corrections to the classical dilaton Kähler potential. If there is a single hidden condensing (simple) gauge group, the axion is massless (up to contributions from higher dimension operators) above the QCD condensation scale. We show how the standard relation between the axion mass and its Planck scale coupling constant is modified in this class of models due to a contribu…
University of Edinburgh（爱丁堡大学）；University of Lethbridge（莱斯布里奇大学）；Indian Statistical Institute（印度统计研究所）；University of Sussex（萨塞克斯大学）；Universidade do Estado do Rio de Janeiro（里约热内卢州立大学）；Massachusetts Institute of Technology（麻省理工学院）
We study the 10D equation of motion of dilaton-axion fluctuations in type IIB string compactifications with three-form flux, taking warping into account. Using simplified models with physics comparable to actual compactifications, we argue that the lightest mode localizes in long warped throats and takes a mass of order the warped string scale. Also, Gukov-Vafa-Witten superpotential is valid for the lightest mass mode; however, the mass is similar to the Kaluza-Klein scale, so the dilaton-axion should be integrated out of the effective theory in this long throat regime (leaving a constant supe…
We study cosmological solutions in the context of 4-dimensional low energy Heterotic M-theory with moving bulk branes. In particular we present non-trivial, analytic axion solutions generated by new symmetries of the full potential-free action which are similar to 'triple axion' solutions found in Pre-Big-Bang (PBB) cosmologies. We also consider the presence of a non-perturbative superpotential, for which we find cosmological solutions with and without a background perfect fluid. In the absence of a fluid the dilaton and the T-modulus go to the potential-free solutions at late time, while the …
We obtain a family of heterotic supergravity backgrounds describing non-Kahler warped conifolds with three-form flux and an Abelian gauge bundle, preserving N=1 supersymmetry in four dimensions. At large distance from the singularity the usual Ricci-flat conifold is recovered. By performing a Z_2 orbifold of the T^{1,1} base, the conifold singularity can be blown-up to a four-cycle, leading to a completely smooth geometry. Remarkably, the throat regions of the solutions, which can be isolated from the asymptotic Ricci-flat geometry using a double-scaling limit, possess a worldsheet CFT descrip…
We study possibilities for lowering the decay constants of superstring axions. In the heterotic Calabi-Yau compactification, a localized model-dependent axion can appear at a nearly collapsing 2-cycle. The effect of flux can be used for generating warp factor suppression of the axion decay constant. We also point out that the hidden sector instanton potential much higher than the QCD instanton potential picks up the larger effective axion decay constant as that of the QCD axion. We show that this can be converted by introducing many hidden-sector quarks so that the decay constant of the QCD ax…
We find that dilaton dominated supersymmetry breaking and spontaneous CP violation can be achieved in heterotic string models with superpotentials singular at the fixed points of the modular group. A semi--realistic picture of CP violation emerges in such models: the CKM phase appears due to a complex VEV of the T-modulus, while the soft supersymmetric CP phases are absent due to an axionic--type symmetry.
We investigate anomalies on heterotic orbifolds and their blowups. We give a simple example of an orbifold blowup which contains anomalous U(1) symmetries that are canceled by axions which couple non-universally to the different gauge groups, thus clarifying some confusion which recently arose in the literature concerning anomaly universality. We argue that non-universal axionic couplings are the general case, and that the couplings are only universal in the case of orbifolds. We comment on the consequences of this non-universality for discrete R symmetries. We furthermore investigate the orig…
We review some exact solitonic solutions of string theory with higher-membrane structure. These include an axionic instanton solution of bosonic string theory as well as multi-instanton and multimonopole solutions of heterotic string theory. The heterotic solutions reveal some interesting aspects of string theory as a theory of quantum gravity.
We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential $C_2$ in the standard Klebanov-Strassler throat. One can think of this inflaton candidate as being defined by the integral of $C_2$ over the $S^2$ cycle of the throat. It obtains an exponentially small mass from the IR-region in which the $S^2$ shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. Crucially, the $S^2$ cycle has to be shared between two throats, such that the second locus where the $S^2$ shrinks is also…
It has recently been appreciated that the conifold modulus plays an important role in string-phenomenological set-ups involving warped throats, both by imposing constraints on model building and for obtaining a 10-dimensional picture of SUSY-breaking. In this note, we point out that the stability of the conifold modulus furthermore prevents large super- Planckian axion monodromy field ranges caused by brane-flux decay processes down warped throats. Our findings imply a significant challenge for concrete string theory embeddings of the inflationary flux-unwinding scenario.
We construct a model of quintessence in string theory based on the idea of axion monodromy as discussed by McAllister, Silverstein and Westphal arXiv:0808.0706. In the model, the quintessence field is an axion whose shift symmetry is broken by the presence of 5-branes which are placed in highly warped throats. This gives rise to a potential for the axion field which is slowly varying, even after incorporating the effects of moduli stabilization and supersymmetry breaking. We find that the resulting time dependence in the equation of state of Dark Energy is potentially detectable, depending on …
Wrapped branes in string compactifications introduce a monodromy that extends the field range of individual closed-string axions to beyond the Planck scale. Furthermore, approximate shift symmetries of the system naturally control corrections to the axion potential. This suggests a general mechanism for chaotic inflation driven by monodromy-extended closed-string axions. We systematically analyze this possibility and show that the mechanism is compatible with moduli stabilization and can be realized in many types of compactifications, including warped Calabi-Yau manifolds and more general Ricc…
We propose a model for large field inflation in heterotic string theory. The construction applies the near alignment mechanism of Kim, Nilles, and Peloso. By including gaugino condensates and world-sheet instanton non-perturbative effects, we obtain a large effective axion decay constant.
Compactifications of heterotic M-theory are shown to provide solutions to the weak- and axion-scale hierarchy problems as a consequence of warped large extra dimensions. They allow a description that is reminiscent of the so-called continuous clockwork mechanism. The models constructed here cover a new region of clockwork parameter space and exhibit unexplored spectra and couplings of Kaluza-Klein modes. Previously discussed models are outside this region of parameter space and do seem to require an ultraviolet completion other than that of perturbative higher dimensional $D=10,11$ string- or …
Calculating Axion-Matter Couplings in String Theory
New York University（纽约大学）；Institute for Advanced Study（高等研究院）；Massachusetts Institute of Technology（麻省理工学院）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
Target space duality (T duality), which interchanges Kaluza--Klein and winding-mode excitations of the compactified heterotic string, is realized as a symmetry of a world-sheet action. Axion-dilaton duality (S duality), a conjectured nonperturbative SL(2,Z) symmetry of the same theory, plays an analogous role for five-branes. We describe a soliton spectrum possessing both duality symmetries and argue that the theory has an infinite number of dual string descriptions.
We discuss R-symmetries in locally supersymmetric N=2 gauge theories coupled to hypermultiplets which can be thought of as effective theories of heterotic superstring models. In this type of supergravities a suitable R-symmetry exists and can be used to topologically twist the theory: the vector multiplet containing the dilaton-axion field has different R-charge assignments with respect to the other vector multiplets. Correspondingly a system of coupled instanton equations emerges, mixing gravitational and Yang--Mills instantons with triholomorphic hyperinstantons and axion-instantons. For the…
We construct spacetime supersymmetric, modular invariant partition functions of strings on the conifold-type singularities which include contributions from the discrete-series representations of SL(2, R). The discrete spectrum is automatically consistent with the GSO projection in the continuous sector, and contains massless matter fields localized on a four-dimensional submanifold at the tip of a cigar. In particular, they are in the 27+1 of E6 for the E8 x E8 heterotic string. We speculate about a possible realization of local E6 GUT by using this framework.
We argue that a new type of extremely light axion is generically present in the type IIB part of the string theory landscape. Its mass is suppressed by the third power of the warp factor of a strongly warped region (Klebanov-Strassler throat), suggesting the name thraxion. Our observation is based on the generic presence of several throats sharing the same 2-cycle. This cycle shrinks to zero volume at the end of each throat. It is hence trivial in homology and the corresponding $C_2$ axion is massive. However, the mass is warping-suppressed since, if one were to cut off the strongly warped reg…
We presented the proof of the positive mass theorem for black holes in Einstein-Maxwell axion-dilaton gravity being the low-energy limit of the heterotic string theory. We show that the total mass of a spacetime containing a black hole is greater or equal to the square root of the sum of squares of the adequate dilaton-electric and dilaton-axion charges.
We compute the new supersymmetric index of a large class of N=2 heterotic compactifications with torsion, corresponding to principal two-torus bundles over warped K3 surfaces with H-flux. Starting from a UV description as a (0,2) gauged linear sigma-model with torsion, we use supersymmetric localization techniques to provide an explicit expression of the index as a sum over the Jeffrey-Kirwan residues of the one-loop determinant. We finally propose a geometrical formula that gives the new supersymmetric index in terms of bundle data, regardless of any particular choice of underlying two-dimens…
We continue our study of codimension two solutions of warped space-time varying compactifications of string theory. In this letter we discuss a non-supersymmetric solution of the classical type IIB string theory with de Sitter gravity on a codimension two uncompactified part of spacetime. A non-zero positive value of the cosmological constant is induced by the presence of non-trivial stringy moduli, such as the axion-dilaton system for the type IIB string theory. Furthermore, the naked singularity of the codimension two solution is resolved by the presence of a small but non-zero cosmological …
We present all the symmetry superalgebras $\mathfrak{g}$ of all warped AdS$_k\times_w M^{d-k}$, $k>2$, flux backgrounds in $d=10, 11$ dimensions preserving any number of supersymmetries. First we give the conditions for $\mathfrak{g}$ to decompose into a direct sum of the isometry algebra of AdS$_k$ and that of the internal space $M^{d-k}$. Assuming this decomposition, we identify all symmetry superalgebras of AdS$_3$ backgrounds by showing that the isometry groups of internal spaces act transitively on spheres. We demonstrate that in type II and $d=11$ theories the AdS$_3$ symmetry superalgeb…
We study a particular N = 1 confining gauge theory with fundamental flavors realised as seven branes in the background of wrapped five branes on a rigid two-cycle of a non-trivial global geometry. In parts of the moduli space, the five branes form bound states with the seven branes. We show that in this regime the local supergravity solution is surprisingly tractable, even though the background topology is non-trivial. New effects such as dipole deformations may be studied in detail, including the full backreactions. Performing the dipole deformations in other ways leads to different warped lo…
Starting with the Taub--NUT solution to Einstein's equations, together with a constant dilaton, a dyonic Taub--NUT solution of low energy heterotic string theory with non--trivial dilaton, axion and $U(1)$ gauge fields is constructed by employing $O(1,1)$ transformations. The electromagnetic dual of this solution is constructed, using $SL(2,\rline)$ transformations. By an appropriate change to scaled variables, the extremal limit of the dual solution is shown to correspond to the low energy limit of an exact conformal field theory presented previously.
In this thesis, we consider heterotic string vacua based on a warped product of a four-dimensional domain wall and a six-dimensional internal manifold preserving only two supercharges. Thus, they correspond to half-BPS states of heterotic supergravity. The constraints on the internal manifolds with SU(3) structure are derived. They are found to be a generalization of half-flat manifolds with a particular pattern of torsion classes and they include half-flat manifolds and Strominger's complex non-Kahler manifolds as special cases. We also verify that heterotic compactifications on half-flat mir…
We study the holographic duals of type II and heterotic matrix string theories described by warped AdS_3 supergravities. By explicitly solving the linearized equations of motion around near horizon D-string geometries, we determine the spectrum of Kaluza-Klein primaries for type I, II supergravities on warped AdS_3 x S^7. The results match those coming from the dual two-dimensional gauge theories living on the D-string worldvolumes. We briefly discuss the connections with the N=(8,8), N=(8,0) orbifold superconformal field theories to which type IIB / heterotic matrix strings flow in the infrar…
We address the question of finding stable and metastable cosmic strings in quasi-realistic heterotic M-theory compactifications with stabilized moduli. According to Polchinski's conjecture, the only stable strings in the absence of massless fields are Aharonov-Bohm strings. Such strings could potentially be created in heterotic compactifications as bound states of open membranes, five-branes wrapped on four-cycles and solitonic strings. However, in generic compactifications, the process of moduli stabilization can conflict production of Aharanov-Bohm strings. In this case, heterotic cosmic str…
N=2 supersymmetric quantum black holes in the heterotic S-T-U model are presented. In particular three classes of axion-free quantum black holes with half the N=2, D=4 supersymmetries unbroken are considered. First, these quantum black holes are investigated at generic points in moduli space. Then linearized non-abelian black holes are investigated representing a subset of non-abelian black hole solutions at critical points of perturbative gauge symmetry enhancement in moduli space. It is shown that the entropy of linearized non-abelian black holes can be obtained, starting at non-critical poi…
We consider d=4 N=2 supergravity theories which serve as low-energy effective actions for heterotic strings on K_3 \times T^2. At the perturbative level we construct a new version of the heterotic effective action in which the axion has been traded for an antisymmetric tensor field. In the string frame the antisymmetric tensor doesn't transform under Poincaré supersymmetry into the dilaton-dilatini system. This indicates that in this frame the antisymmetric tensor field and the dilaton are not contained in an N=2 vector-tensor multiplet. Instead, we find that the heterotic dilaton is part of a…
Rotation angle of the plane of polarization of the distant galactic radio waves has been estimated in a string inspired axion-dilaton background. It is found that the axion,dual to the field strength of the second rank antisymmetric massless Kalb-Ramond field in the string spectrum, produces a wavelength independent optical rotation which is much larger than that produced by the dilaton. Detection of such rotation has been reported in some recent cosmological experiments. The observed value has been compared with our estimated theoretical value following various cosmological constraints. The e…
Mass angular momentum and charge inequalities for axisymmetric maximal time-symmetric initial data invariant under an action of U(1) group, in Einstein-Maxwell-axion-dilaton gravity being the low-energy limit of the heterotic string theory, is established. We assume that data set with two asymptotically flat regions is given on smooth simply connected manifold. We also pay attention to the area momentum charge inequalities for a closed orintabler two-dimensional spacelike surface embedded in the spacetime of the considered theory.
