We continue the study of heterotic non-Abelian BPS-saturated flux tubes (strings). Previously, such solutions were obtained [1] in a particular U(2) gauge theory: N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Here we generalize the previous results to U(N) gauge theories. As was suggested by Edalati and Tong [2], the string world sheet theory is a heterotic N=(0,2) sigma model, with the CP(N-1) target space for bosonic fields and an extra right-handed fermion which couples to the fermion fields of the N=(2,2) CP(N-1) model. We derive the heterotic N=(0,2) world sheet model directly from the U(N) bulk theory. Parameters of the bulk theory are related to those of the world sheet theory. Qualitatively this relation turns out to be the same as in the U(2) case.
We consider non-Abelian BPS-saturated flux tubes (strings) in N=2 supersymmetric QCD deformed by superpotential terms of a special type breaking N=2 supersymmetry down to N=1. Previously it was believed that worldsheet supersymmetry is "accidentally" enhanced due to the facts that N =(1,1) SUSY is automatically elevated up to N=(2,2) on CP(N-1) and, at the same time, there are no N=(0,2) generalizations of the bosonic CP(N-1) model. Edalati and Tong noted that the target space is in fact CP(N-1) x C rather than CP(N-1). This allowed them to suggest a "heterotic" N=(0,2) sigma model, with the C…
A new solution in the string background dual to N=1 SQCD-like theories is presented. The gauge coupling in this solution has walking property. The Wilson loop calculations show that quark anti-quark potential makes phase transitions. Additionally the effect of flavours on other solutions in this background is investigated by considering some unflavoured solutions and perturbing them with small parameter $x=\frac{N_{f}}{N_{c}}$.
The Affleck-Dine-Seiberg instanton generated superpotential for SQCD with Nf=Nc-1 flavours is explicitly derived from a local model of engineered intersecting D6-branes with a single E2-instanton. This computation extends also to symplectic gauge groups with Nf=Nc flavours.
In this paper we make further refinements to the duality proposed between N=1 SQCD and certain string (supergravity plus branes) backgrounds, working in the regime of comparable large number of colors and flavors. Using the string theory solutions, we predict different field theory observables and phenomena like Seiberg duality, gauge coupling and its running, the behavior of Wilson and 't Hooft loops, anomalous dimensions of the quark superfields, quartic superpotential coupling and its running, continuous and discrete anomaly matching. We also give evidence for the smooth interpolation betwe…
We calculate the scalar potential of supersymmetric QCD (in the regime N_f < N_c) coupled to N=1 supergravity with moduli-dependent gauge kinetic function and masses. The gauge dynamics are described by the Taylor-Veneziano-Yankielowicz superpotential for composite effective fields. The potential can be expanded about the ``truncated'' point in the gaugino and matter condensate directions in order to find corrections to the globally supersymmetric minimum. The results are relevant to the phenomenology of supersymmetry-breaking in string-inspired supergravity models, and also to recent work on …
We study the quantum dynamics of vortex strings in N=1 SQCD with U(N_c) gauge group and N_f=N_c quarks. The classical worldsheet of the string has N=(0,2) supersymmetry, but this is broken by quantum effects. We show how the pattern of supersymmetry breaking and restoration on the worldsheet captures the quantum dynamics of the underlying 4d theory. We also find qualitative matching of the meson spectrum in 4d and the spectrum on the worldsheet.
We search for viable models of direct gauge mediation, where the SUSY-breaking sector is (generalized) SQCD, which has cosmologically favorable uplifted vacua even when the reheating temperature is well above the messenger scale. This requires a relatively large tadpole term in the scalar potential for the spurion field X and, consequently, we argue that pure (deformed) SQCD is not a viable model. On the other hand, in SQCD with an adjoint, which is natural e.g. in string theory, assuming an appropriate sign in the Kahler potential for X, such metastable vacua are possible.
We study the String dual to N=1 SQCD deformed by a quartic superpotential in the quark superfields. We present a unified view of the previous results in the literature and find new exact solutions and new asymptotic solutions. Then we study the Physics encoded in these backgrounds, giving among other things a resolution to an old puzzle related to the beta function and a sufficient criteria for screening. We also extend our results to the SO(Nc) case where we present a candidate for the Wilson loop in the spinorial representation. Various aspects of this line of research are critically analyze…
In this note we describe how N=1 SQCD-like theories with a large number of flavors can be given a dual description in terms of a string background containing a large number of additional D5-branes. The dual geometries account for the backreaction of the additional branes: they depend on the ratio between the number of flavors and colors of the gauge theory. This note is based on hep-th/0602027. We present here also a new set of solutions, which are not included in the original paper.
We give a topological classification of stable and unconfined massive particles and strings (and some instantons) in worldvolume theories of M5-branes and their dimensional reductions, generalizing Witten's classification of strings in SYM. In particular 4d N=2 SQCD softly broken to N=1 contains torsion (Douglas-Shenker) Z_N-strings and nontorsion (Hanany-Tong) Z-strings. Some of the former are stable when the flavor symmetry is gauged, while those that are not stable confine quarks and in some vacua even dyons into baryons. The nontorsion strings are stable if and only if all colors are locke…
We consider a model which in a certain limit reduces to the large N ${\cal N}=1$ supersymmetric SU(N) gauge theory without matter. The gaugino condensate in this model is controlled by the dynamics of an additional singlet superfield. Using this model we explicitly construct BPS domain walls arising due to the chiral symmetry breaking. In particular, in the large N limit we obtain the exact shapes of the domain walls corresponding to solitons, and also of the domain walls interpreted as D-branes on which the SQCD string can end, whose existence was previously argued by Witten in the context of…
A glossary overview of the phenomenological studies of quasi-realistic free fermionic heterotic string models is presented. I elaborate on the correspondence of these models with Z2XZ2 orbifolds.
We give a complete classification of Z_N orbifold compactification of the heterotic SO(32) string theory and show its potential for realistic model building. The appearance of spinor representations of SO(2n) groups is analyzed in detail. We conclude that the heterotic SO(32) string constitutes an interesting part of the string landscape both in view of model constructions and the question of heterotic-type I duality.
In the framework of $Z_N$ orbifolds, we discuss effects of heterotic string backgrounds including discrete Wilson lines on the Yukawa matrices and their connection to CP violation.
We consider N=1 supersymmetric quantum chromodynamics (SQCD) with the gauge group U(N_c) and N_c+N quark flavors. N_c flavors are massless; the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra N flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg's dual: U(N) gauge theory with N_c +N flavors of "dual quark" fields plus a gauge-singlet mesonic field M. The original theory is referred to as "quark theory" while the dual one is termed "monopole theory." The suggested mild deformation of Seiberg's pr…
We study soft SUSY breaking terms in heterotic M-theory. We show that both weakly and strongly coupled heterotic string models lead to the same relations of soft SUSY breaking terms, $A=-M$ and $m^2 = M^2/3$, up to $O((αT/S)^2)$.
We construct supergravity plus branes solutions, which we argue to be related to 4d N=1 SQCD with a quartic superpotential. The geometries depend on the ratio Nf/Nc which can be kept of order one, present a good singularity at the origin and are weakly curved elsewhere. We support our field theory interpretation by studying a variety of features like R-symmetry breaking, instantons, Seiberg duality, Wilson loops and pair creation, running of couplings and domain walls. In a second part of this paper, we address a different problem: the analysis of the interesting physics of different members o…
We provide a simple example of dilaton stabilization in the framework of heterotic string theory. It requires a gaugino condensate and an up-lifting sector similar to the one postulated in type IIB string theory. Its signature is a hybrid mediation of supersymmetry breakdown with a variant of a mirage pattern for the soft breaking terms. The set-up is suited for the discussion of heterotic MSSM candidates.
We derive the universal threshold corrections in heterotic string theory including a continuous Wilson line. Unification of gauge and gravitational couplings is shown to be possible even within perturbative string theory. The relative importance of gauge group dependent and independent thresholds on unification is clarified. Equipped with these results we can then attempt an extrapolation to the strongly coupled heterotic string -- M-theory. We argue that such an extrapolation might be meaningful because of the holomorphic structure of the gauge coupling function and the close connection of th…
We investigate the possibility of lowering the string scale in four dimensional heterotic models possessing a non-perturbative extension of the gauge group. In particular, we consider a class of compactifications in which the perturbative gauge sector is massive, and all the gauge bosons are non-perturbative, with a coupling independent on the Planck and string scales.
We study the flavor structure in $SO(32)$ heterotic string theory on six-dimensional torus with magnetic fluxes. In particular, we focus on models with the flavor symmetries $SU(3)_f$ and $Δ(27)$. In both models, we can realize the realistic quark masses and mixing angles.
The three generation heterotic-string models in the free fermionic formulation are among the most realistic string vacua constructed to date, which motivated their detailed investigation. The classification of free fermion heterotic string vacua has revealed a duality under the exchange of spinor and vector representations of the SO(10) GUT symmetry over the space of models. We demonstrate the existence of the spinor-vector duality using orbifold techniques, and elaborate on the relation of these vacua to free fermionic models.
We investigate neutralino dark matter from a string/M-theory perspective. Using the Kallosh-Linde (KL) scenario to stabilize the string moduli requires supersymmetry breaking for uplifting to a de Sitter vacuum. We consider the free magnetic dual description of $\mathcal{N}=1$ SUSY QCD with massive flavours, the Intriligator-Seiberg-Shih model (ISS), as an F-term dynamical SUSY breaking sector. This framework allows for a gravitino mass in the TeV range. Moreover, due to the plethora of particles from the ISS sector, we investigate the consequences of coupling the MSSM with the KL-ISS setup to…
An overview of old and new results in studies of the quasi-realistic free fermionic models is presented, which include the recent discovery of exophobic string vacua and reproduction of the Higgs-matter splitting mechanism in a corresponding orbifold construction.
In T-duality invariant effective supergravity with gaugino condensation as the mechanism for supersymmetry breaking, there is a residual discrete symmetry that could play the role of R-parity in supersymmetric extensions of the Standard Model.
The discovery of the Higgs boson at the LHC supports the hypothesis that the Standard Model provides an effective parameterisation of all subatomic experimental data up to the Planck scale. String theory, which provides a viable perturbative approach to quantum gravity, requires for its consistency the existence of additional gauge symmetries beyond the Standard Model. The construction of heterotic--string models with a viable light $Z^\prime$ is, however, highly constrained. We outline the construction of standard--like heterotic--string models that allow for an additional Abelian gauge symme…
We explore the phenomenological viability of a light Z' in heterotic-string models, whose existence has been motivated by proton stability arguments. A class of quasi-realistic string models that produce such a viable Z' are the Left-Right Symmetric (LRS) heterotic-string models in the free fermionic formulation. A key feature of these models is that the matter charges under U(1)_Z' do not admit an E6 embedding. The light Z' in the LRS heterotic-string models forbids baryon number violating operators, while allowing lepton number violating operators, hence suppressing proton decay yet allowing…
Using Z3 asymmetric orbifolds in heterotic string theory, we construct N=1 SUSY three-generation models with the standard model gauge group SU(3)_C \times SU(2)_L \times U(1)_Y and the left-right symmetric group SU(3)_C \times SU(2)_L \times SU(2)_R \times U(1)_{B-L}. One of the models possesses a gauge flavor symmetry for the Z3 twisted matter.
The spinor-vector duality was discovered in free fermionic constructions of the heterotic-string in four dimensions. It played a key role in the construction of heterotic-string models with an anomaly free extra $Z^\prime$ symmetry that may remain unbroken down to low energy scales. A generic signature of the low scale string derived $Z^\prime$ model is via di-photon excess that may be within reach of the LHC. A fascinating possibility is that the spinor-vector duality symmetry is rooted in the structure of the heterotic-string compactifications to two dimensions. The two dimensional heterotic…
We discuss supersymmetric compactifications of heterotic strings in the presence of H-flux and general condensates using the formalism of G-structures and intrinsic torsion. We revisit the examples based on nearly-Kaehler coset spaces and show that supersymmetric solutions, where the Bianchi identity is satisfied, can be obtained when both gaugino and dilatino condensates are present.
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.
The most promising MSSM candidates of the heterotic string reveal some distinctive properties. These include gauge-top unification, a specific solution to the mu-problem and mirage pattern for the gaugino masses. The location of the top- and the Higgs-multiplets in extra dimensions differs significantly from that of the other quarks and leptons leading to a characteristic signature of suppressed soft breaking terms, reminiscent of a scheme known as natural supersymmetry.
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 investigate the impact of sterile neutrinos on the decay rate of extra $Z'$s with mass in the TeV range in heterotic string derived models. We explore the impact of sterile neutrinos on the current $Z'$ mass exclusion limits at the LHC, and how these bounds change when the parameter space of this specific class of models is modified.
We consider composite string solutions in N=2 SQCD with the gauge group U(N), the Fayet--Iliopoulos term ξ\neq 0 and N (s)quark flavors. These bulk theories support non-Abelian strings and confined monopoles identified with kinks in the two-dimensional world-sheet theory. Similar and more complicated kinks (corresponding to composite confined monopoles) must exist in the world-sheet theories on composite strings. In a bid to detect them we analyze the Hanany--Tong (HT) model, focusing on a particular example of N=2. Unequal quark mass terms in the bulk theory result in the twisted masses in th…
We study the thermodynamics and the jet quenching parameter of a black hole solution dual to a SQCD-like plasma which includes the backreaction of fundamental flavors. The free energy is calculated in several ways, including some recently proposed holographic renormalization prescriptions. The validity of the latter is confirmed by the consistency with the other methods. The resulting thermodynamic properties are similar to the Little String Theory ones: the temperature is fixed at the Hagedorn value and the free energy is vanishing. Finally, an accurate analysis of the relevant string configu…
In a recent paper [1] we showed that N=1 supersymmetric QCD in the presence of certain superpotential deformations has a rich landscape of supersymmetric and non-supersymmetric vacua. In this paper we embed this theory in string theory as a low energy theory of intersecting NS and D-branes. We find that in the region of parameter space of brane configurations that can be reliably studied using classical string theory, the vacuum structure is qualitatively similar to that in the field theory regime. Effects that in field theory come from one loop corrections arise in string theory as classical …
We study vortex-strings in four-dimensional N=2 supersymmetric SU(Nc)xU(1) gauge theories with Nf hypermultiplets in the fundamental representation of SU(Nc) and general U(1) charges. If Nf>Nc, the vacuum is not gapped and the low-energy theory contains both the vacuum massless excitations and the string zero-modes. The question we address in this work is whether the vacuum and the string moduli decouple at low energies, allowing a description of the low-energy dynamics in terms of a two-dimensional theory on the string worldsheet. We find a simple condition controlling the bulk-string couplin…
We explicitly give the correspondence between spectra of heterotic string theory compactified on $T^2$ and string junctions in type IIB theory compactified on $S^2$.
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 classify potential cosmic strings according to the topological charge measurable outside the string core. We conjecture that in string theory it is this charge that governs the stability of long strings. This would imply that the SO(32) heterotic string can have endpoints, but not the E_8 x E_8 heterotic string. We give various arguments in support of this conclusion.
We establish a symmetry map which relates two low-energy heterotic string theories with different numbers of the Abelian gauge fields compactified from the diverse to three dimensions on a torus. We discuss two applications of the established symmetry: a generation of the heterotic string theory solutions from the stationary Einstein-Maxwell fields and one non-trivial submersion of the heterotic string theory into the bosonic one.
We study a new mechanism to dynamically break supersymmetry in the E8xE8 heterotic string. As discussed recently in the literature, a long-lived, meta-stable non-supersymmetric vacuum can be achieved in an N=1 SQCD whose spectrum contains a sufficient number of light fundamental flavors. In this paper, we present, within the context of the hidden sector of the weakly and strongly coupled heterotic string, a slope-stable, holomorphic vector bundle on a Calabi-Yau threefold for which all matter fields are in the fundamental representation and are massive at generic points in moduli space. It is …
We investigate asymmetric orbifold models constructed from non-supersymmetric heterotic strings. We systematically classify the asymmetric orbifold models with standard embeddings and present a list of asymmetric orbifolds which are geometrically interpreted as toroidal compactifications of non-supersymmetric heterotic strings. By studying non-standard embedding models, we also construct examples of the {\em supersymmetric} asymmetric orbifold models based on non-supersymmetric heterotic strings.
We consider the relation between the Ω-deformed N=2 SQCD with the single deformation parameter and integrable models of the BCS-like superconductivity. It is argued that the vortex string worldsheet theory is related to the Russian Doll(RD) model of the truncated BCS superconductivity. We argue that the Ω-deformed gauge theory manifests the interesting cyclic RG behavior with the period of the RG cycle proportional to ε^{-1}. The deformed gauge theory can develop several non-perturbative scales. We conjecture on the monopole bound state interpretation of the Efimov tower.
Type II string theory compactified on a Calabi-Yau manifold, with a singularity modeled by a hypersurface in an orbifold, is considered. In the limit of vanishing string coupling, one expects a non gravitational theory concentrated at the singularity. It is proposed that this theory is holographicly dual to a family of ``non-critical'' superstring vacua, generalizing a previous proposal for hypersurfaces in flat space. It is argued that a class of such singularities is relevant for the study of non-trivial IR fixed points that appear in the moduli space of four-dimensional N=2 SQCD: SU(N_c) ga…
A type IIA string compactified on a Calabi-Yau manifold which admits a K3 fibration is believed to be equivalent to a heterotic string in four dimensions. We study cases where a Calabi-Yau manifold can have more than one such fibration leading to equivalences between perturbatively inequivalent heterotic strings. This allows an analysis of an example in six dimensions due to Duff, Minasian and Witten and enables us to go some way to prove a conjecture by Kachru and Vafa. The interplay between gauge groups which arise perturbatively and nonperturbatively is seen clearly in this example. As an e…
A precise formula for the elliptic genus of three E-strings is presented. The related refined free energy coincides with the result calculated from topological string on local half K3 Calabi-Yau threefold up to genus twelve. The elliptic genus of three heterotic strings computed from M9 domain walls matches with the result from orbifold formula to high orders. This confirms the n=3 case of the recent conjecture that n pairs of E-strings can recombine into n heterotic strings.
A study is made of the implications of heterotic string $T$-duality and extended gauge symmetry for the conjectured equivalence of heterotic and Type I superstrings. While at first sight heterotic string world-sheet dynamics appears to conflict with Type I perturbation theory, a closer look shows that Type I perturbation theory ``miraculously'' breaks down, in some cases via novel mechanisms, whenever the heterotic string has massless particles not present in Type I perturbation theory. This strongly suggests that the two theories actually are equivalent. As further evidence in the same direct…
Brane actions with chiral bosons present special challenges. Recent progress in the description of the two main examples -- the M theory five-brane and the heterotic string -- is described. Also, double dimensional reduction of the M theory five-brane on K3 is shown to give the heterotic string.
Physical aspects of the thermofield dynamics of the D=10 heterotic thermal string theory are exemplified through the infrared behaviour of the one-loop dual symmetric cosmological constant in association with the global phase structure of the thermal string ensemble.
The thermofield dynamics of the D = 10 heterotic thermal string theory is described in proper reference to the thermal duality symmetry as well as the thermal stability of modular invariance in association with the global phase structure of the D = 10 heterotic thermal string ensemble.
We present a class of heterotic compactifications where it is possible to lower the string unification scale down to the GUT scale, while preserving the validity of the perturbative analysis. We illustrate this approach with an explicit example of a four-dimensional chiral heterotic vacuum with N=1 supersymmetry.
Since T-duality has been proved only perturbatively and most of the heterotic states map into solitonic, non-perturbative, type II states, the 6-dimensional string-string duality between the heterotic string and the type II string is not sufficient to prove the S-duality of the former, in terms of the known T-duality of the latter. We nevertheless show in detail that perturbative T-duality, together with the heterotic-type II duality, does imply the existence of heterotic H-monopoles, with the correct multiplicity and multiplet structure. This construction is valid at a generic point in the mo…
Physical aspects of the thermofield dynamics of the D=10 heterotic string theory are exemplified through the infrared behaviour of the one-loop dual symmetric cosmological constant in association with the global phase structure of the thermal string ensemble.
We analyse the BRST cohomology of the Ramond sector of heterotic ambitwistor theory. We also write the free string field theory action and compute the supersymmetry transformations.
