Type 0B String Research Articles

Integrability treatment of AdS/CFT orbifolds

We elaborate on the treatment of orbifolds of type IIB string theory on and their dual gauge theories with integrability techniques. The implementation of orbifolds via twisted spin-chains, thermodynamic Bethe ansatz equations with chemical potentials and Y- and T-systems with modified asymptotics is confronted with twisted boundary conditions of the string sigma-model. This allows us to consistently twist the quantum spectral curve, which is believed to bridge the two sides of the AdS/CFT duality. We discuss Abelian orbifolds of and treat the special cases of supersymmetric -orbifolds and type 0B string theory on as primary examples. This opens a pathway to probe the validity of the duality and to study the long-standing question of tachyon stabilisation in non-supersymmetric AdS/CFT. We comment on the current understanding of this issue and point out the next steps in this challenge.

The S-matrix of 2D type 0B string theory. Part II. D-instanton effects

We study the effect of D-instantons on closed string scattering amplitudes in the two-dimensional type 0B string theory from the worldsheet perspective. We find that the contribution from a pair of D-instanton and anti-D-instanton to the closed string reflection amplitude, with a suitable contour prescription for the integration over the D-instanton moduli space, agrees with the corresponding leading non-perturbative corrections in the proposed dual matrix quantum mechanics. This analysis is further extended to thermal observables defined at finite temperature. The infrared divergence in charged processes is understood through the measure factor for charged D-instantons, and can be treated with spacetime dimensional regularization.

The S-matrix of 2D type 0B string theory. Part I. Perturbation theory revisited

We study the perturbative S-matrix of closed strings in the two-dimensional type 0B string theory from the worldsheet perspective, by directly integrating correlation functions of mathcal{N} = 1 Liouville theory. The latter is computed numerically using recurrence relations for super-Virasoro conformal blocks. We show that the tree level 3- and 4-point amplitudes are in agreement with the proposed dual matrix quantum mechanics. The non-perturbative aspects of the duality will be analyzed in a companion paper.

Infrared finite semi-inclusive cross section in two dimensional type 0B string theory

D-instanton induced S-matrix in type 0B string theory in two dimensions suffers from infrared divergences. This can be traced to the fact that these processes produce low energy rolling tachyon states that cannot be regarded as linear combination of finite number of closed string states. We compute semi-inclusive cross sections in this theory where we allow in the final state a fixed set of closed strings carrying given energies and any number of other closed string states carrying the rest of the energy. The result is infrared finite and agrees with the results in the dual matrix model, described by non-relativistic fermions moving in an inverted harmonic oscillator potential. In the matrix model the role of ‘any number of other closed string states’ is played by a fermion hole pair on opposite sides of the potential barrier.

Normalization of D instanton amplitudes in two dimensional type 0B string theory

We compute the normalization of the D-instanton amplitudes in type 0B string theory in two dimensions and find perfect agreement with the dual matrix model result.

Supersymmetry breaking, brane dynamics and Swampland conjectures

We investigate interactions between branes of various dimensions, both charged and uncharged, in three non-supersymmetric string models. These include the USp(32) and U(32) orientifold projections of the type IIB and type 0B strings, as well as the SO(16)×SO(16) projection of the exceptional heterotic string. The resulting ten-dimensional spectra are free of tachyons, and the combinations of branes that they contain give rise to rich and varied dynamics. We compute static potentials for parallel stacks of branes in three complementary regimes: the probe regime, in which one of the two stacks is parametrically heavier than the other, the string-amplitude regime, in which both stacks are light, and the holographic regime. Whenever comparisons are possible, we find qualitative agreement despite the absence of supersymmetry. For charged branes, our analysis reveals that the Weak Gravity Conjecture is satisfied in a novel way via a renormalization of the effective charge-to-tension ratio.

Phases of U (Nc) QCD3 from type 0 strings and Seiberg duality

We propose an embedding of U(Nc) QCD3 with a Chern-Simons term in string theory. The UV gauge theory lives on the worldvolume of a Hanany-Witten brane configuration in type 0B string theory in the presence of Sagnotti’s O′3 orientifold. We use the brane configuration to propose a magnetic Seiberg dual. We identify various phases of the magnetic theory with conjectured phases of QCD3. In particular the symmetry breaking and bosonization phases are both associated with condensation of the dual squark field. We also discuss the abelian theory without Chern-Simons term and argue that flavour symmetry is not broken. Finally, we also predict novel type 0B string dynamics from QCD dynamics.

A non-supersymmetric large-N3D CFT and its gravity dual

We propose a three dimensional non-supersymmetric theory that is conformal in the large N limit. In a certain well defined bosonic sub-sector of gauge invariant operators, this theory is planar equivalent to the theory recently proposed by Aharony, Bergman, Jafferis and Maldacena as the theory on multiple M2 branes at an orbifold singularity. We discuss the realization of the theory on a brane configuration of type 0B string theory. Moreover, we propose an 11D gravity dual, obtained by a projection of M-theory on AdS4 x S7 / Z_k.

Nonsupersymmetric Seiberg duality, orientifold QCD, and noncritical strings

We propose an electric-magnetic duality and conjecture an exact conformal window for a class of nonsupersymmetric $U({N}_{c})$ gauge theories with fermions in the (anti)symmetric representation of the gauge group and ${N}_{f}$ additional scalar and fermion flavors. The duality exchanges ${N}_{c}\ensuremath{\rightarrow}{N}_{f}\ensuremath{-}{N}_{c}\ensuremath{\mp}4$ leaving ${N}_{f}$ invariant, and has common features with Seiberg duality in $\mathcal{N}=1$ super QCD (SQCD) with $SU$ or $SO/Sp$ gauge group. At large $N$ the duality holds due to planar equivalence with $\mathcal{N}=1$ SQCD. At finite $N$ we embed these gauge theories in a setup with D-branes and orientifolds in a nonsupersymmetric, but tachyon-free, noncritical type 0B string theory and argue in favor of the duality in terms of boundary and crosscap state monodromies as in analogous supersymmetric situations. One can verify explicitly that the resulting duals have matching global anomalies. Finally, we comment on the moduli space of these gauge theories and discuss other potential nonsupersymmetric examples that could exhibit similar dualities.

Noncritical M-theory in 2+1 dimensions as a nonrelativistic Fermi liquid

We claim that the dynamics of noncritical string theories in two dimensions is related to an underlying noncritical version of M-theory, which we define in terms of a double-scaled nonrelativistic Fermi liquid in 2+1 dimensions. After reproducing Type 0A and 0B string theories as solutions, we study the natural M-theory vacuum. The vacuum energy of this solution can be evaluated exactly, its form suggesting a duality to the Debye model of phonons in a melting solid, and a possible topological nature of the theory. The physical spacetime is emergent in this theory, only for states that admit a hydrodynamic description. Among the solutions of the hydrodynamic equations of motion for the Fermi surface, we find families describing the decay of one two-dimensional string theory into another via an intermediate M-theory phase.

A string field theoretical description of (p,q) minimal superstrings

A string field theory of (p,q) minimal superstrings is constructed with the free-fermion realization of 2-component KP (2cKP) hierarchy, starting from 2-cut ansatz of two-matrix models. Differential operators of 2cKP hierarchy are identified with operators in super Liouville theory, and we obtain algebraic curves for the disk amplitudes of \eta=-1 FZZT-branes and the partition functions of neutral/charged \eta=-1 ZZ branes, which correctly reproduce those of type 0B (p,q) minimal superstrings in conformal backgrounds. In the course of study, some subtle points are clarified, including a difference of (p,q) even/odd models and quantization of flux, and we show that the Virasoro constraints naturally incorporate quantized fluxes without ambiguity. We also argue within this string field framework that type 0A minimal superstrings can be obtained by orbifolding the type 0B strings with a Z_2 symmetry existing when special backgrounds are taken.

Thermodynamics of noncritical M-theory and the topological A-model

In [P. Hořava, C.A. Keeler, Noncritical M-theory in 2 + 1 dimensions as a nonrelativistic Fermi liquid, hep-th/0508024], noncritical M-theory for two-dimensional type 0A and 0B strings was defined in terms of a double-scaled theory of nonrelativistic fermions in 2 + 1 dimensions. Here we study this noncritical M-theory at finite temperature. We derive the exact expression for the free energy of its vacuum solution, as a function of a coupling constant g M and the radius R of the thermal circle. We show that at high temperature, the theory is effectively described by another M-theory solution, whose effective loop-counting coupling scales in a novel way characteristic of M-theory, as T 3 . Our calculations further suggest that noncritical M-theory is dual to the closed string theory of the topological A-model on a Calabi–Yau, with the radius R of the Euclidean time circle in M-theory playing the role of the string coupling constant of the A-model. In this correspondence, T-duality on the Euclidean time circle of noncritical M-theory implies an S-duality for the topological A-model.

Topology Changing Transitions in Bubbling Geometries

Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.

Universality of nonperturbative effect in type 0 string theory

We derive the nonperturbative effect in type 0B string theory, which is defined by taking the double scaling limit of a one-matrix model with a two-cut eigenvalue distribution. However, the string equation thus derived cannot determine the nonperturbative effect completely, at least without specifying unknown boundary conditions. The nonperturbative contribution to the free energy comes from instantons in such models. We determine by direct computation in the matrix model an overall factor of the instanton contribution, which cannot be determined by the string equation itself. We prove that it is universal in the sense that it is independent of the detailed structure of potentials in the matrix model. It turns out to be a purely imaginary number and therefore can be interpreted as a quantity related to instability of the D-brane in type 0 string theory. We also comment on a relation between our result and boundary conditions for the string equation.

Unoriented Minimal Type 0 Strings

We define a family of string equations with perturbative expansions that admit an interpretation as an unoriented minimal string theory with background D-branes and R-R fluxes. The theory also has a well-defined non-perturbative sector and we expect it to have a continuum interpretation as an orientifold projection of the non-critical type~0A string for \hat{c}=0, the (2,4) model. There is a second perturbative region which is consistent with an interpretation in terms of background R-R fluxes. We identify a natural parameter in the formulation that we speculate may have an interpretation as characterizing the contribution of a new type of background D-brane. There is a non-perturbative map to a family of string equations which we expect to be the \hat{c}=0 type 0B string. The map exchanges D-branes and R-R fluxes. We present the general structure of the string equations for the (2,4k) type 0A models.

Unitary and Complex Matrix Models as 1-d Type 0 Strings

We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to $\hat c<1 $ matter coupled to super-Liouville theory. We examine in detail the $\hat c=0$ or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on $(2, 4k)$ super-minimal models.

Non-perturbative RR Potentials in the c=1 Matrix Model

We use the \hat c=1 matrix model to compute the potential energy V(C) for (the zero mode of) the RR scalar in two-dimensional type 0B string theory. The potential is induced by turning on a background RR flux, which in the matrix model corresponds to unequal Fermi levels for the two types of fermions. Perturbatively, this leads to a linear runaway potential, but non-perturbative effects stabilize the potential, and we find the exact expression V(C)=\frac{1}{2\pi}\int da\arccos [\cos(C)/\sqrt{1+e^{-2\pi a}}]. We also compute the finite-temperature partition function of the 0B theory in the presence of flux. The perturbative expansion is T-dual to the analogous result in type 0A theory, but non-perturbative effects (which depend on C) do not respect naive R\to 1/R duality. The model can also be used to study scattering amplitudes in background RR fluxes.

A matrix model dual of type 0B string theory in two dimensions

We propose that type 0B string theory in two dimensions admits a dual description in terms of a one dimensional bosonic matrix model of a hermitian matrix. The potential in the matrix model is symmetric with respect to the parity-like Z_2 transformation of the matrix. The two sectors in the theory, namely the NSNS and RR scalar sectors correspond to two classes of operators in the matrix model, even and odd under the Z_2 symmetry respectively. We provide evidence that the matrix model successfully reconstructs the perturbative S-matrix of the string theory, and reproduces the closed string emission amplitude from unstable D-branes. Following recent work in two dimensional bosonic string, we argue that the matrix model can be identified with the theory describing N unstable D0-branes in type 0B theory. We also argue that type 0A theory is described in terms of the quantum mechanics of brane-antibrane systems.

Perturbative and non-perturbative aspects of the two-dimensional string/Yang–Mills correspondence

It is known that YM 2 with gauge group SU( N) is equivalent to a string theory with coupling g s =1/ N, order by order in the 1/ N expansion. We show how this result can be obtained from the bosonization of the fermionic formulation of YM 2, improving on results in the literature, and we examine a number of non-perturbative aspects of this string/YM correspondence. We find contributions to the YM 2 partition function of order exp{− kA/( πα′ g s )} with k an integer and A the area of the target space, which would correspond, in the string interpretation, to D1-branes. Effects which could be interpreted as D0-branes are instead strictly absent, suggesting a non-perturbative structure typical of type 0B string theories. We discuss effects from the YM side that are interpreted in terms of the stringy exclusion principle of Maldacena and Strominger. We also find numerically an interesting phase structure, with a region where YM 2 is described by a perturbative string theory separated from a region where it is described by a topological string theory.

PP-wave and Non-supersymmetric Gauge Theory

We extend the pp-wave correspondence to a non supersymmetric example. The model is the type 0B string theory on the pp-wave R-R background. We explicitly solve the model and give the spectrum of physical states. The field theory counterpart is given by a sector of the large N SU(N) x SU(N) CFT living on a stack of N electric and N magnetic D3-branes. The relevant effective coupling constant is g_{eff}=g_sN/J^2. The string theory has a tachyon in the spectrum, whose light-cone energy can be exactly computed as a function of g_{eff}. We argue that the perturbative analysis in g_{eff} in the dual gauge theory is reliable, with corrections of non perturbative type. We find a precise state/operator map, showing that the first perturbative corrections to the anomalous dimensions of the operators have the behavior expected from the string analysis.