In six dimensions, cancellation of gauge, gravitational, and mixed anomalies strongly constrains the set of quantum field theories which can be coupled consistently to gravity. We show that for some classes of six-dimensional supersymmetric gauge theories coupled to gravity, the anomaly cancellation conditions are equivalent to tadpole cancellation and other constraints on the matter content of heterotic/type I compactifications on K3. In these cases, all consistent 6D supergravity theories have a realization in string theory. We find one example which may arise from a novel string compactification, and we identify a new infinite family of models satisfying anomaly factorization. We find, however, that this infinite family of models, as well as other infinite families of models previously identified by Schwarz are pathological. We suggest that it may be feasible to demonstrate that there is a string theoretic realization of all consistent six-dimensional supergravity theories which have Lagrangian descriptions with arbitrary gauge and matter content. We attempt to frame this hypothesis of string universality as a concrete conjecture.
We show that the quantum corrected string Bethe ansatz passes an important universality test by demonstrating that it correctly incorporates the non-analytical terms in the string sigma model one-loop correction for rational three-spin strings with two out of the three spins identical. Subsequently, we use the quantum corrected string Bethe ansatz to predict the exact form of the non-analytic terms for the generic rational three-spin string.
We exhibit the gauge-group independence (``universality'') of all normalized non-intersecting Wilson loop expectation values in the large N limit of two-dimensional Yang-Mills theory. This universality is most easily understood via the string theory reformulation of these gauge theories. By constructing an isomorphism between the string maps contributing to normalized Wilson loop expectation values in the different theories, we prove the large N universality of these observables on any surface. The string calculation of the Wilson loop expectation value on the sphere also leads to an indicatio…
String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in contrary, there are indications that string theory might be linked to a fundamental principle of a quantum computational character. In addition, the nature of this principle might be capable to provide some new insight into the question of universality of string theory.
We analyze the thermodynamics of NS 5-branes as the temperature approaches the NS 5-branes' Hagedorn temperature, and conclude that the dynamics of ``Little String Theory'' is a new universality class of interacting strings. First we point out how to vary the temperature of the near extremal solution by taking into account $g_s$ corrections. The Hagedorn temperature is shown to be a limiting temperature for the theory. We then compare the thermodynamics to that of a toy model made of free strings and find basic discrepancies. This suggests a need for a new class of string interactions. We sugg…
A recently proposed model of confining strings has a non-local world-sheet action induced by a space-time Kalb-Ramond tensor field. Here we show that, in the large-D approximation, an infinite set of ghost- and tachyon-free truncations of the derivative expansion of this action all lead to c=1 models. Their infrared limit describes smooth strings with world-sheets of Hausdorff dimension D_H=2 and long-range orientational order, as expected for QCD strings.
Nonperturbative effects in c<1 noncritical string theory are studied using the two-matrix model. Such effects are known to have the form fixed by the string equations but the numerical coefficients have not been known so far. Using the method proposed recently, we show that it is possible to determine the coefficients for (p,q) string theory. We find that they are indeed finite in the double scaling limit and universal in the sense that they do not depend on the detailed structure of the potential of the two-matrix model.
Following on from recent studies of string theory on a one-parameter family of integrable deformations of $AdS_{5}\times S^{5}$ proposed by Lunin and Maldacena, we carry out a systematic analysis of the high temperature properties of type IIB strings on the associated pp-wave geometries. In particular, through the computation of the thermal partition function and free energy we find that not only does the theory exhibit a Hagedorn transition in both the $(J,0,0)$ and $(J,J,J)$ class of pp-waves, but that the Hagedorn temperature is insensitive to the deformation suggesting an interesting unive…
We propose that Little String Theories in six dimensions are quasilocal quantum field theories. Such field theories obey a modification of Wightman axioms which allows Wightman functions (i.e. vacuum expectation values of products of fundamental fields) to grow exponentially in momentum space. Wightman functions of quasilocal fields in x-space violate microlocality at short distances. With additional assumptions about the ultraviolet behavior of quasilocal fields, one can define approximately local observables associated to big enough compact regions. The minimum size of such a region can be i…
Exploiting the gauge/gravity correspondence we find the spectrum of hadronic-like bound states of adjoint particles with a large global charge in several confining theories. In particular, we consider an embedding of four-dimensional N=1 supersymmetric Yang-Mills into IIA string theory, two classes of three-dimensional gauge theories and the softly broken version of one of them. In all cases we describe the low energy excitations of a heavy hadron with mass proportional to its global charge. These excitations include: the hadron's nonrelativistic motion, its stringy excitations and excitations…
The hypothesis that every theory of quantum gravity in AdS_3 is a dimensional reduction of string/M-theory leads to a natural conjecture for the density of states of two dimensional CFTs with a large central charge limit. We prove this conjecture for 2D CFTs which are orbifolds by permutation groups. In particular, we characterize those permutation groups which give CFTs with well-defined large N limits and can thus serve as holographic duals to bulk gravity theories in AdS_3. We then show that the holographic dual of a permutation orbifold will have a Hagedorn spectrum in the large N limit. T…
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…
We present a consistency condition for 8d ${\cal N} = 1$ supergravity theories with non-trivial global structure $G/Z$ for the non-Abelian gauge group, based on an anomaly involving the $Z$ 1-form center symmetry. The interplay with other Swampland criteria identifies the majority of 8d theories with gauge group $G/Z$, which have no string theory realization, as inconsistent quantum theories when coupled to gravity. While this condition is equivalent to geometric properties of elliptic K3 surfaces in F-theory compactifications, it constrains the unexplored landscape of gauge groups in other 8d…
Using string field theory, we argue that the tachyon potential on a D-brane anti-D-brane system in type II string theory in arbitrary background has a universal form, independent of the boundary conformal field theory describing the brane. This implies that if at the minimum of the tachyon potential the total energy of the brane antibrane system vanishes in a particular background, then it vanishes in any other background. Similar result holds for the tachyon potential of the non-BPS D-branes of type II string theory, and the D-branes of bosonic string theory.
I review recent work on computing radiative corrections to non-abelian gauge couplings in four-dimensional heterotic vacua with spontaneously broken supersymmetry. The prototype models can be considered as K3 surfaces with additional Scherk-Schwarz fluxes inducing the spontaneous $\mathcal{N}=2 \to \mathcal{N}=0$ breaking. Remarkably, although the gauge thresholds are no longer BPS protected and receive contributions also from the excitations of the RNS sector, their difference is still exactly computable and universal. Based on a talk presented at the DISCRETE 2014 conference at King's Colleg…
In this letter, we provide evidence for universality in the low-energy expansion of tree-level string interactions. More precisely, in the alpha'-expansion of tree-level scattering amplitudes, we conjecture that the leading transcendental coefficient at each order in alpha' is universal for all perturbative string theories. We have checked this universality up to seven points and trace its origin to the ability to restructure the disk integrals of open bosonic string into those of the superstring. The accompanying kinematic functions have the same low-energy limit and do not introduce any tran…
We consider the tree-level scattering amplitudes in the NS-NS (Neveu-Schwarz) massless sector of closed superstrings in the case where one external state becomes soft. We compute the amplitudes generically for any number of dimensions and any number and kind of the massless closed states through the subsubleading order in the soft expansion. We show that, when the soft state is a graviton or a dilaton, the full result can be expressed as a soft theorem factorizing the amplitude in a soft and a hard part. This behavior is similar to what has previously been observed in field theory and in the b…
We consider the strongly coupled limit of conformal gauge theory plasmas with conserved U(1) charges which have a gravity dual. We show that, under mild restrictions, the second order transport coefficients of such theories satisfy a universal relation among themselves, similar to the shear viscosity to entropy ratio.
We discuss the singularities in the moduli space of string compactifications to six dimensions with $N=1$ supersymmetry. Such singularities arise from either massless particles or non-critical tensionless strings. The points with tensionless strings are sometimes phase transition points between different phases of the theory. These results appear to connect all known $N=1$ supersymmetric six-dimensional vacua.
It is shown, by explicit calculation, that the third-order terms in inverse string length in the spectrum of the effective string theories of Polchinski and Strominger are also the same as in Nambu-Goto theory, in addition to the universal Luescher terms. While the Nambu-Goto theory is inconsistent outside the critical dimension, the Polchinski-Strominger theory is by construction consistent for any space-time dimension. In the analysis of the spectrum, care is taken not to use any field redefinition, as it is felt that this has the potential to obscure important points. Nevertheless, as field…
We show that the ${\cal N}=1$ supergravity theories in ten dimensions with gauge groups $U(1)^{496}$ and $E_8 \times U(1)^{248}$ are not consistent quantum theories. Cancellation of anomalies cannot be made compatible with supersymmetry and abelian gauge invariance. Thus, in ten dimensions all supersymmetric theories of gravity without known inconsistencies are realized in string theory.
Present day physics rests on two main pillars: General relativity and quantum field theory. We discuss the deep and at the same time problematic interplay between these two theories. Based on an argument by Doplicher, Fredenhagen, and Roberts, we propose a possible universality property for noncommutative quantum field theory in the sense that any theory of quantum gravity should involve quantum field theories on noncommutative space-times as a special limit. We propose a mathematical framework to investigate such a universality property and start the discussion of its mathematical properties.…
If there is a single underlying "theory of everything" which in some limits of its "moduli space" reduces to the five weakly coupled string theories in 10D, and 11D SUGRA, then it is possible that all six of them have some common domain of validity and that they are in the same universality class, in the sense that the 4D low energy physics of the different theories is the same. We call this notion String Universality. This suggests that the true vacuum of string theory is in a region of moduli space equally far (in some sense) from all perturbative theories, most likely around the self-dual p…
In this letter we study a coupled system of six-dimensional N=1 tensor and super Yang-Mills multiplets. We identify some of the solitonic states of this system which exhibit stringy behaviour in six dimensions. A discussion of the supercharges and energy for the tensor multiplet as well as zero modes is also given. We speculate about the possible relationship between our solution and what is known as tensionless strings.
We study the structure of warped compactifications of type IIB string theory to six space-time dimensions. We find that the most general four-manifold describing the internal dimensions is conformal to a Kahler manifold, in contrast with the heterotic case where the four-manifold must be conformally Calabi-Yau.
Despite recent evidence indicating the existence of a new kind of self-dual six-dimensional superstring, no satisfactory worldsheet formulation of such a string has been proposed. In this note we point out that a theory built from Z_4 parafermions may have the right properties to describe the light-cone conformal field theory of this string. This indicates a possible worldsheet formulation of this theory.
Type IIB strings compactified on K3 have a rich structure of solitonic strings, transforming under SO(21,5,Z). We derive the BPS tension formula for these strings, and discuss their properties, in particular, the points in the moduli space where certain strings become tensionless. By examining these tensionless string limits, we shed some further light on the conjectured dual M-Theory description of this compactification.
We present several classes of new 6d string theories which arise via branes at orbifold singularities. They have compact moduli spaces, associated with tensor multiplets, given by Weyl alcoves of non-Abelian groups. We discuss T-duality and Matrix model applications upon compactification.
As a particle moves through a fluid, it may generate a laminar wake behind it. In the gauge-string duality, we show that such a diffusion wake is created by a heavy quark moving through a thermal plasma and that it has a universal strength when compared to the total drag force exerted on the quark by the plasma. The universality extends over all asymptotically anti-de Sitter supergravity constructions with arbitrary scalar matter. We discuss how these results relate to the linearized hydrodynamic approximation and how they bear on our understanding of di-hadron correlators in heavy ion collisi…
We construct a unique (2,0) supersymmetric action in six dimensions, describing a tensor multiplet interacting with a self-dual string. It is a sum of four terms: A free kinetic term for the tensor multiplet fields integrated over Minkowski space, a Nambu-Goto type kinetic term for the string integrated over the string world-sheet, a Wess-Zumino type electromagnetic coupling integrated over the world-volume of a Dirac membrane attached to the string, and a direct interaction of such Dirac membranes. In addition to supersymmetry, the action is also invariant under a local symmetry, which allows…
We discuss why the N_6=1 heterotic string has to be viewed as something similar to a ``non-compact orbifold''. Only the perturbative spectrum is forced to satisfy the constraints imposed by the vanishing of six-dimensional anomalies. These do not apply to the states of the non-perturbative spectrum, such as those appearing when small instantons shrink to zero size.
We develop an efficient recursive method to evaluate the tachyon potential using the relevant universal subalgebra of the open string star algebra. This method, using off-shell versions of Virasoro Ward identities, avoids explicit computation of conformal transformations of operators and does not require a choice of background. We illustrate the procedure with a pedagogic computation of the level six tachyon potential in an arbitrary gauge, and the evaluation of a few simple star products. We give a background independent construction of the so-called identity of the star algebra, and show how…
We first review the representations of the six-dimensional (2,0) superalgebra on a free tensor multiplet and on a free string. We then construct a supersymmetric Lagrangian describing a free tensor multiplet. (It also includes a decoupled anti self-dual part of the three-form field strength.) This field theory is then rewritten in variables appropriate for analyzing a situation where the R-symmetry is spontaneously broken by the vacuum expectation values of the scalar moduli fields. Finally, we construct a supersymmetric and kappa-symmetric action for a free string.
Recent developments in string theory suggest that string theory landscape of vacua is vast. It is natural to ask if this landscape is as vast as allowed by consistent-looking effective field theories. We use universality ideas from string theory to suggest that this is not the case, and that the landscape is surrounded by an even more vast swampland of consistent-looking semiclassical effective field theories, which are actually inconsistent. Identification of the boundary of the landscape is a central question which is at the heart of the meaning of universality properties of consistent quant…
We investigate a holographic description of k-strings in higher representations via D5 branes with worldvolume fluxes. The D-brane configurations are embedded in supergravity backgrounds dual to confining field theories in 3 and 4 dimensions. We compute the tensions and find qualitative agreement for the totally symmetric and totally anti-symmetric representations with the results of other methods such as lattice as well as the Hamiltonian approach of Karabali and Nair. A one-loop computation on the D-brane configurations yields the Luescher term and allows us to confirm a previously proposed …
We show, by explicit calculation, that the next correction to the universal Luescher term in the effective string theories of Polchinski and Strominger is also universal. We find that to this order in inverse string-length, the ground-state energy as well as the excited-state energies are the same as those given by the Nambu-Goto string theory, the difference being that while the Nambu-Goto theory is inconsistent outside the critical dimension, the Polchinski-Strominger theory is by construction consistent for any space-time dimension. Our calculation explicitly avoids the use of any field red…
We propose here a static and axisymmetric braneworld in six dimensions as a string-like model extension. For a subtle warp function, this scenario provides near brane corrections. By varying the bulk cosmological constant, we obtain a source which passes through different phases. The solution is defined both for the interior as for the exterior of the string and satisfies the weak energy condition. Smooth gravitational massless mode is localized on the brane which core is displaced from the origin. In contrast to the thin string model, the massive solutions have high amplitude near the brane. …
We investigate anomalies on heterotic orbifolds and their blowups. We give a simple example of an orbifold blowup which contains anomalous U(1) symmetries that are canceled by axions which couple non-universally to the different gauge groups, thus clarifying some confusion which recently arose in the literature concerning anomaly universality. We argue that non-universal axionic couplings are the general case, and that the couplings are only universal in the case of orbifolds. We comment on the consequences of this non-universality for discrete R symmetries. We furthermore investigate the orig…
When $N$ five-branes of M-theory coincide the world-volume theory contains tensionless strings, according to Strominger's construction. This suggests a large $N$ limit of tensionless string theories. For the small $E_8$ instanton theories, the definition would be a large instanton number. An adiabatic argument suggests that in the large $N$ limit an effective extra uncompactified dimension might be observed. We also propose ``surface-equations'', which are an analog of Makeenko-Migdal loop-equations, and might describe correlators in the tensionless string theories. In these equations, the ant…
We demonstrate that, due to the finite thickness of domain walls, and the consequent ambiguity in defining their locations, the effective string description obtained by integrating out bulk degrees of freedom contains ambiguities in the coefficients of the various geometric terms. The only term with unambiguous coefficient is the zeroth order Nambu-Goto term. We argue that fermionic ghost fields which implement gauge-fixing act to balance these ambiguities. The renormalized string tension, obtained after integrating out both bulk and world-sheet degrees of freedom, can be defined in a scheme i…
It has recently been conjectured that the type IIA string theory compactified on K3 and the heterotic string theory compactified on a four dimensional torus describe identical string theories. The fundamental heterotic string can be regarded as a non-singular soliton solution of the type IIA string theory with a semi-infinite throat. We show that this solution admits 24 parameter non-singular deformation describing a fundamental heterotic string carrying electric charge and current. The charge is generated due to the coupling of the gauge fields to the anti-symmetric tensor field, and not to a…
We consider an SU(2) gauge theory in six-dimensions. We show that there exists non-trivial structure of gauge vacua in compactified background M4xS2. In this circumstances, there can exist a cosmic string, whose solution is recently constructed by the present authors. We consider the stage of the formation of the strings, i.e., the phase transition of the gauge configuration on the sphere in the `hot' early universe. We find that if SU(2)-doublet fermions are the dominant component of the radiation at high temperatures, the phase transition successively occurs after the spontaneous-compactific…
We study the scattering of low-energy tensor multiplet particles against a BPS saturated cosmic string. We show that the corresponding S-matrix is largely determined by symmetry considerations. We then apply a specific supersymmetric model of (2,0) theory and calculate the scattering amplitudes to lowest non-trivial order in perturbation theory. Our results are valid as long as the energy of the incoming particle is much lower than the square root of the string tension. The calculation involves the quantization of a (2,0) tensor multiplet and the derivation of an effective action describing th…
We discuss branes whose worldvolume dimension equals the target spacetime dimension, i.e. ``spacetime-filling branes''. In addition to the D9-branes, there are 9-branes in the NS-NS sectors of both the IIA and IIB strings. The worldvolume actions of these branes are constructed, via duality, from the known actions of branes with codimension larger than zero. Each of these types of branes is used in the construction of a string theory with sixteen supercharges by modding out a type II string by an appropriate discrete symmetry and adding 32 9-branes. These constructions are related by a web of …
Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理与天文学系马尼·L·巴乌米克理论物理研究所）
We show how recent progress in computing elliptic genera of strings in six dimensions can be used to obtain expressions for elliptic genera of strings in five-dimensional field theories which have a six-dimensional parent. We further connect our results to recent mathematical results about sheaf counting on ruled surfaces.
We propose an organizing principle for classifying and constructing Schrodinger-invariant solutions within string theory and M-theory, based on the idea that such solutions represent nonlinear completions of linearized vector and graviton Kaluza-Klein excitations of AdS compactifications. A crucial simplification, derived from the symmetry of AdS, is that the nonlinearities appear only quadratically. Accordingly, every AdS vacuum admits infinite families of Schrodinger deformations parameterized by the dynamical exponent z. We exhibit the ease of finding these solutions by presenting three new…
We construct the first rotating string solution in 6-dimensional Einstein-Gauss-Bonnet supergravity, carrying both electric and magnetic charges. By embedding the known rotating string solution of the 2-derivative theory into 6-dimensional off-shell supergravity, the Killing spinors associated with the underlying supersymmetry can be made off-shell and are universal to all off-shell supergravity models based on the same field content. The near-horizon geometry is S^3 fibred over the extremal BTZ black hole, locally isomorphic to AdS_3*S^3. We compute the higher-derivative corrections to the Br…
This article is based on a talk given at the ``Strings'97'' conference. It discusses the search for the universality class of confining strings. The key ingredients include the loop equations, the zigzag symmetry, the non-linear renormalization group. Some new tests for the equivalence between gauge fields and strings are proposed.
We extend our analysis of the soft behaviour of string amplitudes with massive insertions to closed strings at tree level (sphere). Relying on our previous results for open strings on the disk and on KLT formulae we check universality of the soft behaviour for gravitons to sub-leading order for superstring amplitudes and show how this gets modified for bosonic strings. At sub-sub-leading order we argue in favour of universality for superstrings on the basis of OPE of the vertex operators and gauge invariance for the soft graviton. The results are illustrated by explicit examples of 4-point amp…
We consider scattering of minimally coupled scalars from a six-dimensional black string carrying one and five brane charges but no Kaluza-Klein momentum. The leading correction to the absorption cross section is found by improved matching of inner and outer solutions to the wave equation. The world sheet interpretation of this correction follows from the breaking of conformal invariance by irrelevant Born-Infeld corrections. We note that discrepancies in normalisation are caused by there being two effective length scales in the black string geometry but only one in the effective string model a…
We consider the (2, 0) supersymmetric theory of tensor multiplets and self-dual strings in six space-time dimensions. Space-time diffeomorphisms that leave the string world-sheet invariant appear as gauge transformations on the normal bundle of the world-sheet. The naive invariance of the model under such transformations is however explicitly broken by anomalies: The electromagnetic coupling of the string to the two-form gauge field of the tensor multiplet suffers from a classical anomaly, and there is also a one-loop quantum anomaly from the chiral fermions on the string world-sheet. Both of …
We consider Dotsenko-Fateev matrix models associated with compactified Calabi-Yau threefolds. They can be constructed with the help of explicit expressions for refined topological vertex, i.e. are directly related to the corresponding topological string amplitudes. We describe a correspondence between these amplitudes, elliptic and affine type Selberg integrals and gauge theories in five and six dimensions with various matter content. We show that the theories of this type are connected by spectral dualities, which can be also seen at the level of elliptic Seiberg-Witten integrable systems. Th…
We analyse the trapping of eigenspinors of the charge conjugation operator with dual helicity (Elko), in thin and thick string-like models with codimension-2. Elko spinor fields describe mass dimension one fermions in four dimensions (and, correspondingly, mass dimension two fermions in six dimensions), that represent natural dark matter prime candidates. This dark spinor has many applications, from particle physics to cosmology. On the other hand, six-dimensional brane-world models have, among other prominent features, the spontaneous confinement of free spin 1 fields and a mechanism that exp…
We propose a candidate for the dual (in the weak/strong coupling sense) of the six-dimensional heterotic string compactification constructed recently by Chaudhuri, Hockney and Lykken. It is a type IIA string theory compactified on an orbifold $K3/Z_2$, where the $Z_2$ action involves an involution of $K3$ with fixed points, and also has an embedding in the U(1) gauge group associated with the Ramond-Ramond sector of the type IIA string theory. This introduces flux of the U(1) gauge field concentrated at the orbifold points. This construction provides an explicit example where the dual of a sup…
Quantum anomalies, determined by the Atiyah-Singer index theorem, place strong constraints on the space of quantum gravity theories in six dimensions with minimal supersymmetry. The conjecture of "string universality" states that all such theories which do not have anomalies or other quantum inconsistencies are realized in string theory. This paper describes this conjecture and recent work by Kumar, Morrison, and the author towards developing a global picture of the space of consistent 6D supergravities and their realization in string theory via F-theory constructions. We focus on the discrete…
In theories with extended supersymmetry the protected observables of UV superconformal fixed points are found in a number of contexts to be encoded in the BPS solitons along an IR Coulomb-like phase. For six-dimensional SCFTs such a role is played by the BPS strings on the tensorial Coulomb branch. In this paper we develop a uniform description of the worldsheet theories of a BPS string for rank-one 6d SCFTs. These strings are the basic constituents of the BPS string spectrum of arbitrary rank six-dimensional models, which they generate by forming bound states. Motivated by geometric engineeri…
In the framework of heterotic compactifications, we consider the one-loop corrections to the gauge couplings, which were shown to be free of any infra-red ambiguity. For a class of N=2 models, namely those that are obtained by toroidal compactification to four dimensions of generic six-dimensional N=1 ground states, we give an explicit formula for the gauge-group independent thresholds, and show that these are equal within this class, as a consequence of an anomaly-cancellation constraint in six dimensions. We further use these results to compute the (N=2)-sector contributions to the threshold…
