We discuss a novel strategy to construct 4D N=0 stable flux vacua of type II string theory, based on the existence of BPS bounds for probe D-branes in some of these backgrounds. In particular, we consider compactifications where D-branes filling the 4D space-time obey the same BPS bound as they would in an N=1 compactification, while other D-branes, like those appearing as domain walls from the 4D perspective, can no longer be BPS. We construct a subfamily of such backgrounds giving rise to 4D N=0 Minkowski no-scale vacua, generalizing the well-known case of type IIB on a warped Calabi-Yau. We provide several explicit examples of these constructions, and compute quantities of phenomenological interest like flux-induced soft terms on D-branes. Our results have a natural, simple description in the language of Generalized Complex Geometry, and in particular in terms of D-brane generalized calibrations. Finally, we extend the integrability theorems for 10D supersymmetric type II backgrounds to the N=0 case and use the results to construct a new class of N=0 AdS4 compactifications.
We derive algebraic attractor equations describing supersymmetric flux vacua of type IIB string theory in terms of the doublet of the 3-form fluxes, F and H. These equations are similar to the attractor equations for moduli fixed by the charges near the horizon of the supersymmetric black holes.
We consider two infinite families of Non-Supersymmetric $AdS_4$ vacua, called Type 2) and Type 3) vacua, that arise in massive IIA supergravity with flux. We show that both families are perturbatively stable. We then examine non-perturbative decays of these vacua to other supersymmetric and non-supersymmetric $AdS_4$ vacua mediated by instantons in the thin wall approximation. We find that many decays are ruled out since the tension of the interpolating domain wall is too big compared to the energy difference in AdS units. In fact, within our approximations no decays of Type 2) vacua are allow…
We present a detailed analysis of non-supersymmetric spacetime varying string vacua which can lead to an exponential hierarchy between the electroweak and the gravitational scales. In particular, we identify a limit in which these vacua can be interpreted as supersymmetric vacua of F-theory. Furthermore, we study the properties of these solutions as seen by $D7$-brane probes and establish a non-supersymmetric analogue of the enhancon mechanism.
We construct new families of non-supersymmetric sourceless type IIA AdS4 vacua on those coset manifolds that also admit supersymmetric solutions. We investigate the spectrum of left-invariant modes and find that most, but not all, of the vacua are stable under these fluctuations. Generically, there are also no massless moduli.
Supersymmetric Minkowski vacua in IIB orientifold compactifications based on orbifolds with background fluxes and non-perturbative superpotentials are investigated. Especially, microscopic requirements and difficulties to obtain such vacua are discussed. We show that orbifold models with one and two complex structure moduli and supersymmetric 2-form flux can be successfully stabilized to such vacua. By taking additional gaugino condensation on fixed space-time filling D3-branes into account also models without complex structure can be consistently stabilized to Minkowski vacua.
We study the supersymmetric vacua of the Veneziano-Wosiek model in sectors with fermion number F=2, 4 at finite 't Hooft coupling lambda. We prove that for F=2 there are two zero energy vacua for lambda > lambda_c = 1 and none otherwise. We give the analytical expressions of both vacua. One of them was previously known, the second one is obtained by solving the cohomology of the supersymmetric charges. At F=4 we compute the would-be supersymmetric vacua at high order in the the strong coupling expansion and provide strong support to the conclusion that lambda = 1 is a critical point in this se…
In the context of supersymmetric Wess-Zumino models with an R symmetry, we find some simple conditions on the R-charge content of the theory that imply the presence or absence of supersymmetric and R-symmetric vacua. The main result of this work is that the comparison between the number of R-charge 0 and R-charge 2 superfields is essential to the properties of the model as regards symmetry breaking. We also study possible exceptions to the Nelson-Seiberg theorem --finding that there are supersymmetric vacua that break R symmetry in generic models-- and the spontaneous breaking of R symmetry in…
It has recently been argued that the confining vacua of Yang-Mills theory in the far infrared can have topological degrees of freedom given by magnetic $\mathbb{Z}_q$ gauge field, both in the non-supersymmetric case and in the N=1 supersymmetric case. In this short note we give another piece of evidence by computing and matching the supersymmetric index of the pure super Yang-Mills theory both in the ultraviolet and in the infrared.
We find the complete chiral ring relations of the supersymmetric U(N) gauge theories with matter in adjoint representation. We demonstrate exact correspondence between the solutions of the chiral ring and the supersymmetric vacua of the gauge theory. The chiral ring determines the expectation values of chiral operators and the low energy gauge group. All the vacua have nonzero gaugino condensation. We study the chiral ring relations obeyed by the gaugino condensate. These relations are generalizations of the formula $S^N=Λ^{3N}$ of the pure ${\cal N} =1$ gauge theory.
We study $N=1$ supersymmetric $SP(N_c)$ gauge theories with $N_f$ flavors of quarks in the fundamental representation. Depending on $N_f$ and $N_c$, we find exact, dynamically generated superpotentials, smooth quantum moduli spaces of vacua, quantum moduli spaces of vacua with additional massless composites at strong coupling, confinement without chiral symmetry breaking, non-trivial fixed points of the renormalization group, and massless magnetic quarks and gluons.
Some N=1 gauge theories, including SQED and N_F=1 SQCD have the property that, for arbitrary superpotentials, all stationary points of the potential V = F+D are D-flat. For others, stationary points of V are complex gauge transformationss of D-flat configurations. As an implication, the technique to parametrize the moduli space of supersymmetric vacua in terms of a set of basic holomorphic G invariants can be extended to non-supersymmetric vacua. A similar situation is found in non-gauge theories with a compact global symmetry group.
We review open descendants of non-supersymmetric type IIB asymmetric orbifolds with zero cosmological constant. We find that supersymmetry remains unbroken on the branes at all mass levels, whereas it is broken in the bulk.
We investigate models of SU(N) SQCD with adjoint matter and non trivial mesonic deformations. We apply standard methods in the dual magnetic theory and we find meta-stable supersymmetry breaking vacua with arbitrary large lifetime. We comment on the difference with known models.
We study a class of N=1 supersymmetric U(N) gauge theories and find that there exist vacua in which the low-energy magnetic effective gauge group contains multiple nonabelian factors, \prod_i SU(r_i), supported by light monopoles carrying the associated nonabelian charges. These nontrivially generalize the physics of the so-called r-vacua found in softly broken N=2 supersymmetric SU(N) QCD, with an effective low-energy gauge group SU(r) \times U(1)^{N-r}. The matching between classical and quantum (r_{1}, r_{2},...) vacua gives an interesting hint about the nonabelian duality.
An explicit proof of the existence of nontrivial vacua in the pure supersymmetric Yang-Mills theories with higher orthogonal SO(N), N>=7 or the G_2 gauge group defined on a 3-torus with periodic boundary conditions is given. Extra vacuum states are separated by an energy barrier from the perturbative vacuum A_i=0 and its gauge copies.
We consider a wide class of cascading gauge theories which usually lead to runaway behaviour in the IR, and discuss possible deformations of the superpotential at the bottom of the cascade which stabilize the runaway direction and provide stable non-supersymmetric vacua. The models we find may allow for a weakly coupled supergravity analysis of dynamical supersymmetric breaking in the context of the gauge/string correspondence.
Reducing Supersymmetric Yang-Mills Field Theory to a single point in the three dimensional space results in the Supersymmetric Yang-Mills Quantum Mechanics (SYMQM) which basically is the effective quantum mechanics of zero momentum modes of the original theory. Such a system is still quite non-trivial and usually inherits many properties of the original field theory. In this talk some beautiful features of the three-dimensional model will be reviewed and illustrated with the aid of the recent, quantitative solution. In particular the structure of the supersymmetric vacua and condensates will b…
We perform a systematic search for anti-de Sitter vacua of maximal supergravity with N>2 residual supersymmetries. We find that maximal supergravity admits two 1-parameter classes of N=3 and N=4 vacua, respectively. They are embedded, for the different values of an angular parameter, in the $ω$-rotated SO(8) (N=3) and SO(1,7) (N=4 and 3) gauged models. All vacua disappear in the limit when $ω$ tends to zero. We determine the mass spectra and the AdS-supermultiplet structure. These appear to be the first and only N>2 supersymmetric AdS vacua in maximal supergravity, aside from the N=8 vacua of …
We derive an exact unified formula for all condensates (quark and monopole) in the hybrid r vacua in N=2 supersymmetric QCD slightly deformed by a μA^2 term. The gauge group is assumed to be U(N) and the number of the quark flavors N_f subject to the condition N< N_f < 2N. In the r vacua r quarks and N-r-1 monopoles from non-overlapping subgroups of U(N) develop vacuum expectation values (r<N). We then briefly review possible dynamical regimes (confinement, screening, and "instead of confinement") in the hybrid r vacua in μ-deformed N=2 SQCD (the small-μlimit).
Anomalous U(1)s are omnipresent in realizations of the Standard Model using D-branes. Such models are typically non-supersymmetric, and the anomalous U(1) masses are potentially relevant for experiment. In this paper, the string calculation of anomalous U(1) masses (hep-th/0204153) is extended to non-supersymmetric orientifolds.
We classify the N=4 supersymmetric AdS5 backgrounds that arise as solutions of five-dimensional N=4 gauged supergravity. We express our results in terms of the allowed embedding tensor components and identify the structure of the associated gauge groups. We show that the moduli space of these AdS vacua is of the form SU(1,m)/(U(1)x SU(m)) and discuss our results regarding holographically dual N=2 SCFTs and their conformal manifolds.
We study the SO(3)-invariant relevant deformations of N=4 SU(N) gauge theory using the methods of Polchinski and Strassler. We present the region of parameter space where the non-supersymmetric vacuum is still described by stable ``dielectric'' five branes within the supergravity approximation.
We review the construction of non-supersymmetric open string vacua in various dimensions. They can be obtained either projecting the (compactified) non-supersymmetric 0B theory, or applying the Scherk-Schwarz mechanism to open strings. Generically, these vacua generate a non-vanishing cosmological constant. However, one can construct particular kinds of Scherk-Schwarz compactifications with vanishing cosmological constant, at least for low orders, based on asymmetric orbifolds. A generic feature of these models is that supersymmetry remains unbroken on the branes at all mass level, while it is…
We count the supersymmetric vacua of mass-deformed N=6 U(N)xU(N) Chern-Simons-matter theory by calculating the Witten index. When the Chern-Simons level k is 1, our result perfectly agrees with that from the gravity dual, given by partitions of N. For general k, our index generalizes partitions of N, including additional degrees. We also comment on non-relativistic superconformal theories constructed from this model.
We present a construction of modular invariant partition functions for heterotic (0,2) supersymmetric classical string vacua. This generalization of Gepner's construction yields GUT gauge groups E_6, SO(10), SU(5) and SU(3) x SU(2) x U(1)^r, respectively. By calculating the massless spectrum of some of these models we find strong indications that they correspond to (0,2) string vacua discussed recently in the context of CYM/LG phases.
We conjecture that all vacua in string theory decay. More precisely, non-supersymmetric vacua in string theory are at most metastable and eventually decay, while supersymmetric vacua are only marginally stable. All de Sitter vacua with small cosmological constant are metastable to decay via a process that occurs on scales small compared to the horizon size.
Exact black hole solutions of the five dimensional heterotic $S$-$T$-$U$ model including all perturbative quantum corrections and preserving $1/2$ of $N=2$ supersymmetry are studied. It is shown that the quantum corrections yield a bound on electric charges and harmonic functions of the solutions.
We consider genuine type IIB string theory (supersymmetric) brane intersections that preserve $(1+1)$D Lorentz symmetry. We provide the full supergravity solutions in their analytic form and discuss their physical properties. The Ansatz for the spacetime dependence of the different brane warp factors goes beyond the harmonic superposition principle. By studying the associated near-horizon geometry, we construct interesting classes of AdS$_3$ vacua in type IIB and highlight their relation to the existing classifications in the literature. Finally, we discuss their holographic properties.
Following a suggestion made by Tseytlin, we investigate the case when one replaces the transverse part of the bosonic action by an $n=2$ supersymmetric sigma-model with a symmetric homogeneous Kählerian target space. As conjectured by Tseytlin, the metric is shown to be exactly known since the beta function is known to reduce to its one-loop value.
We classify the non-supersymmetric, and perturbatively stable within $D=4$, AdS vacua of maximal $D=4$ supergravity with a dyonic ISO(7) gauging in a large sector of the supergravity. Seven such vacua are established within this sector, all of them giving rise to non-supersymmetric $\textrm{AdS}_{4} \times \textrm{S}^{6}$ type IIA backgrounds with and without non-trivial warpings and with internal fluxes. Then, we analyse the dynamics of various probe D$p$-branes in these backgrounds searching for potential brane-jet instabilities. In all these cases, such instabilities are absent. Finally, an…
We provide explicit formulas for the number of vacua of four-dimensional pure N=1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. These form a key ingredient in the semi-classical calculation of the number of massive vacua of N=1* gauge theories with gauge algebra su(n) compactified on a circle. Using arithmetic, we express that number in an SL(2,Z) duality invariant manner. We confirm our tally of massive vacua of the N=1* theories by a count of inequivalent extrema of the exact superpotential. Furthermore, we compu…
Making use of non-perturbative U-duality symmetries of type II strings we construct new `superstring' vacua in three dimensions with N=1 supersymmetry. This has an interpretation as compactifying formally from 13 dimensions (S-theory) on Calabi-Yau 5-folds possessing a $T^3 \x T^2$ fibration. We describe some part of the massless multiplets, given by the Hodge spectrum, and point to a corresponding 5-brane configuration.
We study AdS backgrounds of N=4 supergravity in four space-time dimensions which preserve all sixteen supercharges. We show that the graviphotons have to form a subgroup of the gauge group that consists of an electric and a magnetic SO(3)_+ x SO(3)_-. Moreover, these N=4 AdS backgrounds are necessarily isolated points in field space which have no moduli.
We analyze non-supersymmetric four dimensional open string models of type IIB string theory compactified on $T^2\times K3$ with Scherk-Schwarz deformation acting on an $S^1$ of the $T^2$ torus. We find that there are always two solutions to the tadpole conditions that are shown to be connected via Wilson lines in an non-trivial way. These models although non-supersymmetric, are free of R-R and NS-NS tadpoles.
We study fully supersymmetric $AdS_6$ vacua of half-maxi\-mal $N=(1,1)$ gauged supergravity in six space-time dimensions coupled to $n$ vector multiplets. We show that the existence of $AdS_6$ backgrounds requires that the gauge group is of the form $G'\times G"\subset SO(4,n)$ where $G'\subset SO(3,m)$ and $G"\subset SO(1,n-m)$. In the $AdS_6$ vacua this gauge group is broken to its maximal compact subgroup $SO(3)\times H'\times H"$ where $H'\subset SO(m)$ and $H"\subset SO(n-m)$. Furthermore, the $SO(3)$ factor is the R-symmetry gauged by three of the four graviphotons. We further show that …
We discuss stability of non-supersymmetric compactification of M-theory and string theory of the form AdS * X, and their dual non-supersymmetric interacting conformal field theories. We argue some of the difficulties in controlling 1/N-corrections disappear in the cases that the large-N dual conformal field theory has no invariant marginal operators (and in some cases with no exactly marginal operators only). We provide several examples of such compactifications of M-theory down to AdS4.
We study the correspondence between the moduli space of vacua of three-dimensional supersymmetric Yang-Mills (Maxwell) Chern-Simons theories and brane configurations with (p,q)5-brane. For Coulomb branches, the number of the massless adjoint scalar fields in various supersymmetric theories exactly coincides with the number of the freely moving directions of D3-branes stretched between two 5-branes. When we include a matter superfield into the supersymmetric Chern-Simons theory two distinct symmetric and asymmetric phase appear. The symmetric phase is peculiar to this Chern-Simons Higgs system.…
Supersymmetric vacua are stable. It is interesting to ask: how long-lived are vacua which are nearly supersymmetric? This question is relevant if our universe is approximately supersymmetric. It is also of importance for a number of issues of the physics of the landscape and eternal inflation. In this note, we distinguish a variety of cases. In all of them the decay is slow. For a flat space theory decaying to a deep AdS vacuum, the leading behavior of the decay amplitude, if a thin wall approximation is valid, is ${\cal A} = γe^{-2 π^2/({\rm Re} m_{3/2})^2}$ (where the phase of $m_{3/2}$ is d…
We show that the maximally supersymmetric vacua of d=5 N=1 sugra remain maximally supersymmetric solutions when taking into account higher order corrections.
It has recently been conjectured that string theory does not admit de Sitter critical points. This note points out that in several cases, including KKLT or racetrack models, this statement is equivalent to the absence of supersymmetric Minkowski or AdS solutions. This equivalence arises from establishing the positivity of the potential in a large-radius limit, requiring a turnover of the potential before reaching an AdS vacuum. For example, this conjecture is incompatible with the simplest 1-modulus KKLT AdS supersymmetric solution.
We consider N=1 supersymmetric QCD based on the G_2 gauge group and including 3 chiral matter 7-plets. In that case, the gauge symmetry is broken completely and the instanton-generated superpotential on the classical moduli space is present. If the theory involves the Yukawa term, there are six chirally asymmetric vacua. In the limit when the Yukawa coupling vanishes, two of the vacua run away to infinity and only 4 asymmetric vacuum states are left. Besides, a chirally symmetric state is always present. We consider also an O(7) model with 4 chiral multiplets in spinor representation. In that …
The moduli space of the supersymmetric massive IIA AdS4xS2(B4) vacua, where S2(B4) is a two-sphere bundle over a four-dimensional Kaehler-Einstein base B4, includes three independent parameters which can be thought of as corresponding to the sizes of AdS4, B4 and the S2 fiber. It might therefore be expected that these vacua do not suffer from the absence of scale separation. We show that the independence of the geometric moduli survives flux quantization. However, we uncover an attractor behavior whereby all sizes flow to equality in some neighborhood of spacetime independently of the initial …
We classify the supersymmetric vacua of N=4, d=5 supergravity in terms of G-structures. We identify three classes of solutions: with R^3, SU(2) and generic SO(4) structure. Using the Killing spinor equations, we fully characterize the first two classes and partially solve the latter. With the N=4 graviton multiplet decomposed in terms of N=2 multiplets: the graviton, vector and gravitino multiplets, we obtain new supersymmetric solutions corresponding to turning on fields in the gravitino multiplet. These vacua are described in terms of an SO(5) vector sigma-model coupled with gravity, in thre…
We study two-dimensional N=(4,4) supersymmetric gauge theories which do not have classical Higgs branches, but are believed to have isolated quantum Higgs vacua. We provide arguments for the existence of such vacua based on brane dynamics in string theory and the supersymmetric partition sums of the gauge theories.
We find non-supersymmetric metastable vacua in four dimensional N=2 gauge theories softly broken to N=1 by a superpotential term. First we study the simplest case, namely the SU(2) gauge theory without flavors. We study the spectrum and lifetime of the metastable vacuum and possible embeddings of the model in UV complete theories. Then we consider larger gauge group theories with flavors. We show that when we softly break them to N=1, the potential induced on specific submanifolds of their moduli space is identical to the potential in lower rank gauge theories. Then we show that the potential …
We consider generic properties of the moduli space of vacua in $N=2$ supersymmetric Yang--Mills theory recently studied by Seiberg and Witten. We find, on general grounds, Picard--Fuchs type of differential equations expressing the existence of a flat holomorphic connection, which for one parameter (i.e. for gauge group $G=SU(2)$), are second order equations. In the case of coupling to gravity (as in string theory), where also ``gravitational'' electric and magnetic monopoles are present, the electric--magnetic S duality, due to quantum corrections, does not seem any longer to be related to $S…
In supersymmetric models with the run-away vacua or with the stable but non-supersymmetric ground state there exist stable field configurations (vacua) which restore one half of supersymmetry and are characterized by constant positive energy density. The formal foundation for such vacua is provided by the central extension of the N =1 superalgebra with the infinite central charge.
We study supersymmetric AdS$_7$ vacua of massive type IIA string theory, which were argued to describe the near-horizon limit of NS5/D6/D8-brane intersections and to be holographically dual to 6D $(1,0)$ theories. We show, for the case without D8-brane charges, that such vacua do not admit any supersymmetry-breaking deformations. Our result implies that the dual $(1,0)$ theories do not have a conformal manifold, thus extending previously known results for supersymmetric deformations. It is also in line with the recent conjecture that non-supersymmetric AdS vacua are in the swampland.
We consider backgrounds of (massive) IIA supergravity of the form of a warped product $M_{1,3}\times_ω X_6$, where $X_6$ is a six-dimensional compact manifold and $M_{1,3}$ is $AdS_4$ or a four-dimensional Minkowski space. We analyse conditions for $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.
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 show how to construct supersymmetric warped AdS$_7$ vacua of massive IIA and AdS$_6$ vacua of IIB supergravity, using "half-maximal structures" of exceptional field theory. We use this formalism to obtain the minimal consistent truncations around these AdS vacua.
On the Type IIB toroidal T^6 orientifolds with generic flux compactifications, we conjecture that in generic supsersymmetric Minkowski vacua, at least one of the flux contributions to the seven-brane and D3-brane tadpoles is positive if the moduli are stabilized properly, and then the tadpole cancellation conditions can not be relaxed. To study the supsersymmetric Minkowski flux vacua, we simplify the fluxes reasonably and discuss the corresponding superpotential. We show that we can not have simultaneously the positive real parts of all the moduli and the negative/zero flux contributions to a…
We construct configurations of NS-, D4-, and D6-branes in type IIA string theory, realizing the recently discussed non-supersymmetric meta-stable minimum of 4d N=1 SU(N_c) super-Yang-Mills theories with massive flavors. We discuss their lift to M-theory and the mechanism of pseudo-moduli stabilization. We extend the construction to many other examples of meta-stable minima, including the SO/Sp theories, SU(N_c) with matter in two-index tensor representations, and to a chiral gauge theory.
This is an announcement of some of the results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The correspondence between the Heisenberg spin chain and the two dimensional U(N) theory with fundamental hypermultiplets is reviewed in detail. We demonstrate the isomorphism of the equivariant quantum cohomology of the cotangent bundle to the Grassmanian manifold Gr(N,L) and the ring of quantum integrals of motion of the length L SU(2) XXX …
We argue that tachyon-free type I string vacua with supersymmetry breaking in the open sector at the string scale can be interpreted, via S and T-duality arguments, as metastable vacua of supersymmetric type I superstring. The dynamics of the process can be partially captured via nucleation of brane-antibrane pairs out of the non-supersymmetric vacuum and subsequent tachyon condensation.
