We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing -- connecting the two E_8 boundaries by a throat -- are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E_8 gauge group and a singlet tachyon. We then use worldsheet methods to study the tachyon condensation in the NSR formulation of this model, and show that it induces a worldsheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for worldsheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the worldsheet gravitino assimilates the goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R_ξgauges, and note the importance of logarithmic CFT in the context of tachyon condensation.
We calculate partition functions for supersymmetric heterotic theories on Melvin background with Wilson line. These functions coincide with partition functions for some of non-supersymmetric heterotic theories in appropriate limits. This suggests that non-supersymmetric heterotic theories are equivalent to supersymmetric theories on supersymmetry-breaking backgrounds, just as in the case of recently conjectured IIA-0A duality.
We show how to construct the familiar heterotic NS5 brane as a topological soliton in a supercritical version of heterotic string theory. Closed string tachyon condensation removes the extra dimensions, leaving the NS5 in 10d, in a process highly reminiscent of the K-theoretical description of type II D-branes, but linking non-trivial gauge bundles and geometry. The construction requires a modification of the anomalous Bianchi identity for $H_3$ in supercritical heterotic string theory. We give various proofs for the existence of this modification.
We study exact string backgrounds representing a constant magnetic field background in heterotic string theory. These backgrounds are obtained by Kaluza-Klein reduction of a special class of plane wave solutions. For small values of the magnetic field they possess localized closed string tachyons analogous to the Nielsen-Olesen instability of a constant magnetic field in SO(3) Yang-Mills theory. When the magnetic field is embedded in the SO(32) gauge group of the heterotic string it is possible to study the lowest level tachyon in supergravity. We identify the closed string tachyons as fluctua…
Perturbative heterotic string theory develops a single complex tachyonic mode beyond the Hagedorn temperature. We calculate the quartic effective potential for this tachyonic mode at the critical temperature. Equivalently, we determine the quartic effective potential for strong supersymmetric breaking via anti-perdiodic boundary conditions for fermions on a small circle. We give many details of the heterotic tachyon scattering amplitudes, including a unitarity check to fix all normalization constants. We discuss difficulties in obtaining an effective action valid at all radii. We argue that in…
We consider C/Z_N and C^2/Z_N orbifolds of heterotic string theories and Z_N orbifolds of AdS_3. We study theories with N=2 worldsheet superconformal invariance and construct RG flows. Following Harvey, Kutasov, Martinec and Moore, we compute g_cl and show that it decreases monotonically along RG flows- as conjectured by them. For the heterotic string theories, the gauge degrees of freedom do not contribute to the computation of g_cl.
Recently it was proposed that ten-dimensional tachyonic string vacua may serve as starting points for the construction of viable four dimensional phenomenological string models which are tachyon free. This is achieved by projecting out the tachyons in the four-dimensional models using projectors other than the projector which is utilised in the supersymmetric models and those of the $SO(16)\times SO(16)$ heterotic string. We continue the exploration of this class of models by developing systematic computerised tools for their classification, the analysis of their tachyonic and massless spectra…
The $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic string orbifold yielded a large space of phenomenological three generation models and serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. In this paper we explore the existence of type 0 models in this class of string compactifications. We demonstrate the existence of type 0 $\mathbb{Z}_2\times \mathbb{Z}_2$ heterotic string orbifolds, and show that there exist a large degree of redundancy in the space of GGSO projection coefficients when the type 0 restrictions are …
Recently it was proposed that the ten dimensional tachyonic superstring vacua may serve as good starting points for the construction of viable phenomenological models. Such phenomenologically viable models enlarge the space of possible string solutions, and may offer novel insight into some of the outstanding problems in string phenomenology. In this paper we present a three generation standard--like model that may be regarded as a compactification of a ten dimensional tachyonic vacuum. We discuss the features of the model as compared to a similar model that may be regarded as compactification…
In this talk we review recent investigations of the non-supersymmetric heterotic SO(16)xSO(16) string on orbifolds and smooth Calabi-Yaus. Using such supersymmetry preserving backgrounds allows one to re-employ commonly known model building techniques. We will argue that tachyons do not appear on smooth Calabi-Yaus to leading order in alpha' and g_s. Twisted tachyons may arise on singular orbifolds, where some of these approximations break down. However, they get lifted in full blow-up. Finally, we show that model searches is viable by identifying over 12,000 of SM-like models on various orbif…
Maximal Enhancements in Eight-Dimensional Non-Supersymmetric Heterotic Strings
Kyushu University（九州大学）；Institute for Advanced Study, Kyushu University（九州大学高等研究院）；Quantum and Spacetime Research Institute (QuaSR), Kyushu University（量子与时空研究所（QuaSR），九州大学）
We discuss the condensation of charged tachyons in the heterotic theory on the Kaluza-Klein Melvin background. The arguments are based on duality relations which are expected to hold from the adiabatic argument. It is argued that in many cases the rank of the gauge group is not changed by the condensation, as opposed to naive expectations.
We consider tachyon condensation in unstable ten-dimensional heterotic string theory with gauge group E8. In the background of a lightlike linear dilaton rolling to weak coupling, we find an exact solution in which the theory decays to a stable ground state. The final state represents a new, modular-invariant perturbative string theory, tachyon-free in nine spacetime dimensions with a spacelike dilaton gradient, E8 gauge group and no spacetime supersymmetry.
We investigate orbifold and smooth Calabi-Yau compactifications of the non-supersymmetric heterotic SO(16)xSO(16) string. We focus on such Calabi-Yau backgrounds in order to recycle commonly employed techniques, like index theorems and cohomology theory, to determine both the fermionic and bosonic 4D spectra. We argue that the N=0 theory never leads to tachyons on smooth Calabi-Yaus in the large volume approximation. As twisted tachyons may arise on certain singular orbifolds, we conjecture that such tachyonic states are lifted in the full blow-up. We perform model searches on selected orbifol…
We extend the classification of fermionic $\mathbb{Z}_2\times\mathbb{Z}_2$ heterotic string orbifolds to non--supersymmetric Pati--Salam (PS) models in two classes of vacua, that we dub $\tilde S$--models and $S$--models. The first correspond to compactifications of a tachyonic ten--dimensional vacuum, whereas the second correspond to compactifications of the ten--dimensional tachyon--free $SO(16)\times SO(16)$ heterotic string. In both cases we develop a systematic method to extract tachyon--free four--dimensional models. We show that tachyon--free configurations arise with probability $\sim0…
Dilaton contact terms in the bosonic and heterotic strings are examined following the recent work of Distler and Nelson on the bosonic and semirigid strings. In the bosonic case dilaton two-point functions on the sphere are calculated as a stepping stone to constructing a `good' coordinate family for dilaton calculations on higher genus surfaces. It is found that dilaton-dilaton contact terms are improperly normalized, suggesting that the interpretation of the dilaton as the first variation of string coupling breaks down when other dilatons are present. It seems likely that this can be attribu…
The heterotic--string models in the free fermionic formulation gave rise to some of the most realistic string models to date, which possess N=1 spacetime supersymmetry. Lack of evidence for supersymmetry at the LHC instigated recent interest in non-supersymmetric heterotic-string vacua. We explore what may be learned in this context from the quasi--realistic free fermionic models. We show that constructions with a low number of families give rise to proliferation of a priori tachyon producing sectors, compared to the non--realistic examples, which typically may contain only one such sector. Th…
Several principal aspects of a theoretical approach to the theory of faster-than-light particles (tachyons) are considered in this note. They concern the resolution of such problems of tachyon theory as the causality violation by tachyons, the stability of the tachyon vacuum, and the stability of ordinary particles against the spontaneous emission of tachyons, i.e. the problems which are generally used as arguments against the possibility of such particles. It is demonstrated that all these arguments contain nontrivial loopholes which undermine their validity. A demand for a consistent tachyon…
An exact conformal model representing a constant magnetic field background in heterotic string theory is explicitly solved in terms of free creation/annihilation operators. The spectrum of physical states is examined for different possible embeddings of the magnetic U(1) subgroup. We find that an arbitrarily small magnetic field gives rise to an infinite number of tachyonic excitations corresponding to charged vector states of the massless level and to higher level states with large spins and charges.
Alternative gauge choices for worldsheet supersymmetry can elucidate dynamical phenomena obscured in the usual superconformal gauge. In the particular example of the tachyonic $E_8$ heterotic string, we use a judicious gauge choice to show that the process of closed-string tachyon condensation can be understood in terms of a worldsheet super-Higgs effect. The worldsheet gravitino assimilates the goldstino and becomes a dynamical propagating field. Conformal, but not superconformal, invariance is maintained throughout.
Closed string theories on orbifolds contain both untwisted and twisted states. The latter are normally assumed to live exactly at the orbifold fixed points. We perform a calculation of a gauge field tadpole amplitude and show that off-shell both the twisted and untwisted states give rise to non-trivial momentum profiles over the orbifold C^3/Z_3. These profiles take the form of Gaussian distributions integrated over the fundamental domain of the modular parameter of the torus. The propagators of the internal coordinate fields on the torus world sheet determine the width of the Gaussian profile…
We consider backreaction due to production of massless strings in the background of a condensing closed string tachyon. Working in the region of weak tachyon, we find the modified equations of motion for massless strings with conformal perturbation theory. We solve for the positive and negative frequency modes and estimate the backreaction on the background dilaton. In large (supercritical) dimensions, we find that the backreaction can be significant in a large region of spacetime. We work with the bosonic string, but we expect these results to carry over into the heterotic case.
We find that the gas of IIA strings undergoes a phase transition into a gas of IIB strings at the self-dual temperature. A gas of free heterotic strings undergoes a Kosterlitz-Thouless duality transition with positive free energy and positive specific heat but vanishing internal energy at criticality. We examine the consequences of requiring a tachyon-free thermal string spectrum. We show that in the absence of Ramond-Ramond fluxes the IIA and IIB string ensembles are thermodynamically ill-defined. The 10D heterotic superstrings have nonabelian gauge fields and in the presence of a temperature…
In heterotic string theories consistency requires the introduction of a non-trivial vector bundle. This bundle breaks the original ten-dimensional gauge groups $\text{E}_8\times\text{E}_8$ or $\text{SO}(32)$ for the supersymmetric heterotic string theories and $\text{SO}(16) \times \text{SO}(16)$ for the non-supersymmetric tachyon-free theory to smaller subgroups. A vast number of MSSM-like models have been constructed up to now, most of which describe the vector bundle as a sum of line bundles. However, there are several different ways of describing these line bundles and their embedding in t…
We re-examine the question of heterotic - heterotic string duality in six dimensions and argue that the $E_8\times E_8$ heterotic string, compactified on $K3$ with equal instanton numbers in the two $E_8$'s, has a self-duality that inverts the coupling, dualizes the antisymmetric tensor, acts non-trivially on the hypermultiplets, and exchanges gauge fields that can be seen in perturbation theory with gauge fields of a non-perturbative origin. The special role of the symmetric embedding of the anomaly in the two $E_8$'s can be seen from field theory considerations or from an eleven-dimensional …
We study a family of unstable heterotic string theories in more than ten dimensions which are connected via tachyon condensation to the ten-dimensional supersymmetric vacuum of heterotic string theory with gauge group SO(32). Calculating the spectrum of these theories, we find evidence for an S-duality which relates type I string theory in ten dimensions with n additional ninebrane-antininebrane pairs to heterotic string theory in 10+n dimensions with gauge group SO(32+n). The Kaluza-Klein modes of the supercritical dimensions are dual to non-singlet bound states of open strings.
We extend strong/weak coupling duality to string theories without spacetime supersymmetry, and focus on the case of the unique ten-dimensional, nonsupersymmetric, tachyon-free $SO(16)\times SO(16)$ heterotic string. We construct a tachyon-free heterotic string model that interpolates smoothly between this string and the ten-dimensional supersymmetric $SO(32)$ heterotic string, and we construct a dual for this interpolating model. We find that the perturbative massless states of our dual theories precisely match within a certain range of the interpolation. Further evidence for this proposed dua…
One of the goals of the landscape program in string theory is to extract information about the space of string vacua in the form of statistical correlations between phenomenological features that are otherwise uncorrelated in field theory. Such correlations would thus represent predictions of string theory that hold independently of a vacuum-selection principle. In this paper, we study statistical correlations between two features which are likely to be central to any potential description of nature at high energy scales: gauge symmetries and spacetime supersymmetry. We analyze correlations be…
We discuss what information can be safely extracted from background independent off-shell string theory. The major obstacle in doing so is that renormalization conditions of the underlying world-sheet theories are not exactly known. To get some insight, we first consider the tachyon and gauge field backgrounds and carry out computations in different renormalization schemes for both, bosonic string and superstring. Next, we use a principle of universality (renormalization scheme independence) to somehow compensate the missing of the renormalization conditions and get information we are looking …
A few nine-dimensional interpolating models with two parameters are constructed and the massless spectra are studied by considering compactification of heterotic strings on a twisted circle with Wilson line. It is found that there are some conditions between radius R and Wilson line A under which the gauge symmetry is enhanced. In particular, when the gauge symmetry is enhanced to SO(18) \times SO(14), the cosmological constant is exponentially suppressed. We also construct a non-supersymmetric string model which is tachyon-free in all regions of moduli space and whose gauge symmetry involves …
In a tachyon model proposed by Minahan and Zwiebach and derived in the boundary string field theory, we construct various new solutions which correspond to nontrivial brane configurations in string theory. Our solutions include Dp-D(p-2) bound states, (F, Dp) bound states, string junctions, D(p-2)-branes ending on a Dp-brane, D(p-2)-branes suspended between parallel Dp-branes and their non-commutative generalizations. We find the Bogomol'nyi bounds and the BPS equations for some of our solutions, and check the physical consistency of our solutions with the D-brane picture by looking at the dis…
Recent developments in string theory have reinforced the notion that the space of stable supersymmetric and non-supersymmetric string vacua fills out a ``landscape'' whose features are largely unknown. It is then hoped that progress in extracting phenomenological predictions from string theory -- such as correlations between gauge groups, matter representations, potential values of the cosmological constant, and so forth -- can be achieved through statistical studies of these vacua. To date, most of the efforts in these directions have focused on Type I vacua. In this note, we present the firs…
Inspired by the tachyon-free non-supersymmetric heterotic SO(16)xSO(16) string we consider a special class of non-supersymmetric field theories: Those that can be obtained from supersymmetric field theories by supersymmetry breaking twists. We argue that such theories, like their supersymmetric counter parts, may still possess some fermionic symmetries as left-overs of the super gauge transformations and have special one-loop non-renormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking…
Both the supersymmetric $SO(32)$ and $E_8\times E_8$ heterotic strings in ten dimensions have known strong-coupling duals. However, it has not been known whether there also exist strong-coupling duals for the non-supersymmetric heterotic strings in ten dimensions. In this paper, we construct explicit open-string duals for the circle-compactifications of several of these non-supersymmetric theories, among them the tachyon-free $SO(16)\times SO(16)$ string. Our method involves the construction of heterotic and open-string interpolating models that continuously connect non-supersymmetric strings …
The $Z_2\times Z_2$ heterotic string orbifold gives rise to a large space of phenomenological three generation models that serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of quantum gravity. Recently, we demonstrated the existence of type 0 $Z_2\times Z_2$ heterotic string orbifolds in which there are no massless fermionic states. In this paper we demonstrate the existence of non--supersymmetric tachyon--free $Z_2\times Z_2$ heterotic string orbifolds that do not contain any massless bosonic states from the twisted sectors. We du…
I argue that the ten dimensional non--supersymmetric tachyonic superstrings may serve as good starting points for the construction of viable phenomenological vacua. Thus, enlarging the space of possible solutions that may address some of the outstanding problems in string phenomenology. A tachyon free six generation Standard--like Model is presented, which can be regarded as an orbifold of the $SO(16)\times E_8$ heterotic--string in ten dimensions. I propose that any $(2,0)$ heterotic--string in four dimensions can be connected to a $(2,2)$ one via an orbifold or by interpolations and provide …
We present a pedagogical review of the stable non-BPS states in string theory which have recently attracted some attention in the literature. In particular, following the analysis of A. Sen, we discuss in detail the case of the stable non-BPS D-particle of Type I theory whose existence is predicted (and required) by the heterotic/Type I duality. We show that this D-particle originates from an unstable bound state formed by a D1/anti-D1 pair of Type IIB in which the tachyon field acquires a solitonic kink configuration. The mechanism of tachyon condensation is discussed first at a qualitative l…
We examine the fluctuations around a Dp-brane solution in an unstable D-brane system using boundary states and also boundary string field theory. We show that the fluctuations correctly reproduce the fields on the Dp-brane. Plugging these into the action of the unstable D-brane system, we recover not only the tension and RR charge, but also full effective action of the Dp-brane exactly. Our method works for general unstable D-brane systems and provides a simple proof of D-brane descent/ascent relations under the tachyon condensation. In the lowest dimensional unstable D-brane system, called K-…
We show that non-Abelian discrete symmetries in orbifold string models have a gauge origin. This can be understood when looking at the vicinity of a symmetry enhanced point in moduli space. At such an enhanced point, orbifold fixed points are characterized by an enhanced gauge symmetry. This gauge symmetry can be broken to a discrete subgroup by a nontrivial vacuum expectation value of the Kähler modulus $T$. Using this mechanism it is shown that the $Δ(54)$ non-Abelian discrete symmetry group originates from a $SU(3)$ gauge symmetry, whereas the $D_4$ symmetry group is obtained from a $SU(2)$…
In some string theories, e.g. SO(32) heterotic string theory on Calabi-Yau manifolds, a massless field with a tree level potential can acquire a tachyonic mass at the one loop level, forcing us to quantize the theory around a new background that is not a solution to the classical equations of motion and hence is not described by a conformally invariant world-sheet theory. We describe a systematic procedure for carrying out string perturbation theory around such backgrounds.
The tachyon-free nonsupersymmetric string theories in ten dimensions have dilaton tadpoles which forbid a Minkowski vacuum. We determine the maximally symmetric backgrounds for the $USp(32)$ Type I string and the $SO(16)\times SO(16)$ heterotic string. The static solutions exhibit nine dimensional Poincaré symmetry and have finite 9D Planck and Yang-Mills constants. The low energy geometry is given by a ten dimensional manifold with two boundaries separated by a finite distance which suggests a spontaneous compactification of the ten dimensional string theory.
We show that the recent world-sheet analysis of the quantum fluctuations of a short flux tube in type II string theory leads to a simple and precise description of a pair of stuck D0branes in an orientifold compactification of the type I' string theory. The existence of a stable type I' flux tube of sub-string-scale length is a consequence of the confinement of quantized flux associated with the scalar dualized ten-form background field strength *F_{10}, evidence for a -2brane in the BPS spectrum of M theory. Using heterotic-type I duality, we infer the existence of an M2brane of finite width …
In this paper, we discuss the important question of how to extrapolate a given zero-temperature string model to finite temperature. It turns out that this issue is surprisingly subtle, and we show that many of the standard results require modification. For concreteness, we focus on the case of the ten-dimensional SO(32) heterotic string, and show that the usual finite-temperature extrapolation for this string is inconsistent at the level of a proper worldsheet theory. We then derive the proper extrapolation, and in the process uncover a universal Hagedorn temperature for all tachyon-free close…
We study tree-level solutions to heterotic string theory in which the number of spacetime dimensions 10+n changes dynamically due to closed string tachyon condensation. Taking the large-n limit, we compute the amount by which the dilaton gradient changes during the condensation process. At leading order in n we find that the change in the invariant magnitude of the dilaton gradient compensates the change in spacelike central charge on the worldsheet, so that the total worldsheet central charges are equal at early and late times. This result supports our interpretation of the worldsheet theory …
This thesis contributes with a number of topics to the subject of string compactifications. In the first half of the work, I discuss the Hodge plot of Calabi-Yau threefolds realised as hypersurfaces in toric varieties. The intricate structure of this plot is explained by the existence of certain webs of elliptic-K3 fibrations. Such manifolds arise from reflexive polytopes that can be cut into two parts along K3 slices. Any two half-polytopes over a given slice can be combined into a reflexive polytope. This fact, together with a remarkable relation on the additivity of Hodge numbers, give to t…
