We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to tree amplitudes in toroidal compactifications of string theory to four dimensions. The closed string tree amplitudes with massless external states respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8) R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses on two aspects: (i) We provide a detailed account of the simplest SU(8)-violating amplitudes. We classify these processes and derive explicit superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4) symmetry at order alpha'^3. Their origin is the dilatonic operator exp(-6 phi) R^4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order alpha'^3 and use two different methods to isolate the SU(8)-singlet contribution from exp(-6 phi) R^4. This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R^4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N=8 supergravity candidate counterterm R^4 is incompatible with continuous E_7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R^4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.
We present the complete map of any pair of super Yang-Mills theories to supergravity theories as dictated by the KLT relations in four dimensions. Symmetries and the full set of associated vanishing identities are derived. A graphical method is introduced which simplifies counting of states, and helps in identifying the relevant set of symmetries.
Institute for Particle and Nuclear Physics, Charles University（查尔斯大学粒子与核物理研究所）；Center for Quantum Mathematics and Physics (QMAP), University of California, Davis（加州大学戴维斯分校量子数学与物理中心）
Tensionless string theory on AdS3 x S3 x T4, as captured by a free symmetric product orbifold, has a large set of conserved currents which can be usefully organised in terms of representations of a N=(4,4) supersymmetric higher spin algebra. In this paper we focus on the single particle currents which generate the asymptotic stringy symmetry algebra on AdS3, and whose wedge modes describe the unbroken gauge symmetries of string theory in this background. We show that this global subalgebra contains two distinct higher spin algebras that generate the full algebra as a `higher spin square'. The …
The high-energy limit of stringy symmetries, derived from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string, are used to reproduce Gross's linear relations among high-energy scattering amplitudes of different string states with the same momenta. Moreover, the proportionality constants between scattering amplitudes of different string states are calculated for the first few low-lying levels. These proportionality constants are, as suggested by Gross from the saddle point calculation of high-energy string-loop amplitudes, …
We derive stringy symmetries with conserved charges of arbitrarily high spins from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. These symmetries are valid to all energy and all loop orders in string perturbation theory. The high-energy limit of these stringy symmetries can then be used to fix the proportionality constants between scattering amplitudes of different string states algebraically without referring to Gross and Mende's saddle point calculation of high-energy string-loop amplitudes. These proportionality …
We present scattering of stringy states of closed bosonic string compactified on d-dimensional torus. We focus our attention on scattering of moduli and gauge bosons. These states appear when massless excitations such as graviton and antisymmetric tensor field of the uncompactified theory are dimensionally reduced to lower dimension. The toroidally compactified theory is endowed with the T-duality symmetry, O(d,d). Therefore, it is expected that the amplitude for scattering of such states will be $T$-duality invariant. The formalism of Kawai-Llewelen-Tye is adopted and appropriately tailored t…
We consider the simplest possible setting of non abelian twist fields which corresponds to $SU(2)$ monodromies. We first review the theory of hypergeometric function and of the solutions of the most general Fuchsian second order equation with three singularities. Then we solve the problem of writing the general solution with prescribed $U(2)$ monodromies. We use this result to compute the classical string solution corresponding to three $D2$ branes in $R^4$. Despite the fact the configuration is supersymmetric the classical string solution is not holomorphic. Using the equation of motion and n…
We identify spacetime symmetry charges of 26D open bosonic string theory from an infinite number of zero-norm states (ZNS) with arbitrary high spin in the old covariant first quantized string spectrum. We give various evidences to support this identification. These include massive sigma-model calculation, Witten string field theory calculation, 2D string theory calculation and, most importantly, three methods of high-energy stringy scattering amplitude calculations. The last calculations explicitly prove Gross's conjectures in 1988 on high energy symmetry of string theory.
The quantum symmetry of many \LG\ orbifolds appears to be broken by Yang-Mills instantons. However, isolated Yang-Mills instantons are not solutions of string theory: They must be accompanied by gauge anti-instantons, gravitational instantons, or topologically non-trivial configurations of the $H$ field. We check that the configurations permitted in string theory do in fact preserve the quantum symmetry, as a result of non-trivial cancellations between symmetry breaking effects due to the various types of instantons. These cancellations indicate new constraints on \LG\ orbifold spectra and req…
We study three-dimensional consistent truncations of type IIB supergravity which admit warped AdS$_3$ solutions. These theories contain subsectors that have no bulk dynamics. We show that the symplectic form for these theories, when restricted to the non-dynamical subsectors, equals the symplectic form for pure Einstein gravity in AdS$_3$. Consequently, for each consistent choice of boundary conditions in AdS$_3$, we can define a consistent phase space in warped AdS$_3$ with identical conserved charges. This way, we easily obtain a Virasoro $\times$ Virasoro asymptotic symmetry algebra in warp…
We study the origin of non-Abelian discrete flavor symmetries in superstring theory. We classify all possible non-Abelian discrete flavor symmetries which can appear in heterotic orbifold models. These symmetries include D_4 and Delta(54). We find that the symmetries of the couplings are always larger than the symmetries of the compact space. This is because they are a consequence of the geometry of the orbifold combined with the space group selection rules of the string. We also study possible breaking patterns. Our analysis yields a simple geometric understanding of the realization of non-Ab…
Discrete symmetries play a crucial role in particle physics. They appear abundantly in string model constructions. We focus here on the case of discrete $R$-symmetries which are intrinsically connected to the Lorentz group in extra dimensions and the appearance of $N$-extended supersymmetry. In that sense, discrete $R$-symmetries can be understood as "fractionally" extended supersymmetry. These symmetries reveal insight about the location of fields in extra dimensions (in particular the Higgs boson). Applications can be found in the solution of the $μ$-problem, suppression of proton decay and …
We point out that the moduli sector of the $(2,2)$ string compactification with its nonperturbatively preserved non-compact symmetries is a framework to study global topological defects. Based on the target space modular invariance of the nonperturbative superpotential of the four-dimensional $N=1$ supersymmetric string vacua, topologically stable stringy domain walls are found. Explicit supersymmetric solutions for the modulus field and the metric, which saturate the Bogomol'nyi bound, are presented. They interpolate between {\it non-degenerate} vacua. As a corollary, this defines a new notio…
Motivated by the search for a space-time supersymmetric extension of the N=2 string, we construct a particle model which, upon quantization, describes (abelian) self-dual super Yang-Mills in 2+2 dimensions. The local symmetries of the theory are shown to involve both world-line supersymmetry and kappa symmetry.
In the low-energy limit, string theory has two remarkable symmetries, O(d,d+p) and SL(2,R). We illustrate the use of these transformations as techniques to generate new solutions by applying them to the Taub--NUT metric.
We give a simplified method to generate two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. Zero-norm states up to the fourth massive level and general formulas of some zero-norm tensor states at an arbitrary mass level are calculated. On-shell Ward identities generated by zero-norm states and the factorization property of stringy vertex operators can then be used to argue that the string-tree scattering amplitudes of the degenerate lower spin propagating states are fixed by those of higher spin propagating states at each fixed mass level.…
There are many conceivable possibilities of embedding the MSSM in string theory. These proceedings describe an approach which is based on grand unification in higher dimensions. This allows one to obtain global string-derived models with the exact MSSM spectrum and built-in gauge coupling unification. It turns out that these models exhibit various appealing features such as (i) see-saw suppressed neutrino masses, (ii) an order one top Yukawa coupling and potentially realistic flavor structures, (iii) non-Abelian discrete flavor symmetries relaxing the supersymmetric flavor problem, (iv) a hidd…
We study the minimal flavor violation in the context of string effective field theory. Stringy selection rules indicate that $n$-point couplings among fermionic zero-modes and lightest scalar modes in the string effective action are given by a product of Yukawa couplings which are regarded as spurion fields of stringy and geometrical symmetries. Hence, Yukawa couplings determine the dynamics of flavor and CP violations. This observation strongly supports the hypothesis of minimal flavor violation in the Standard Model effective field theory.
We derive stringy Ward identities from the decoupling of two types of zero-norm states in the old covariant first quantized (OCFQ) spectrum of open bosonic string. These Ward identities are valid to all energy and all loop orders in string perturbation theory. The high-energy limit of these stringy Ward identities can then be used to fix the proportionality constants between scattering amplitudes of different string states algebraically without referring to Gross and Mende's saddle point calculation of high-energy string-loop amplitudes. As examples, all Ward identities for the mass level 4 an…
We construct a "stringy" version of Newton-Cartan gravity in which the concept of a Galilean observer plays a central role. We present both the geodesic equations of motion for a fundamental string and the bulk equations of motion in terms of a gravitational potential which is a symmetric tensor with respect to the longitudinal directions of the string. The extension to include a non-zero cosmological constant is given. We stress the symmetries and (partial) gaugings underlying our construction. Our results provide a convenient starting point to investigate applications of the AdS/CFT correspo…
The holomorphy of the superpotential along with symmetries gives very strong constraints on any stringy non-perturbative effects. This observation suggests an approach to string phenomenology. (Presented at ``Strings 95'', March 1995.
An empirically successful mass formula derived long ago from hadronic string models is not explained by symmetries of the QCD lagrangian. Consider that M(rho)^2-M(pi)^2 = M(K*)^2-M(K)^2 to a few percent accuracy. We derive this and other equal spacing relations using chiral symmetry and a novel Z_2 symmetry. We offer an interpretation of this Z_2 symmetry as a manifestation of chiral anomalies in a gauge theory with an intrinsic cutoff.
Duality between the `axion' field $a$ and the antisymmetric tensor field $B_{μν}$ is traced after a nonperturbative effect, gaugino condensation, breaks the Peccei-Quinn symmetry $a \rightarrow a +c$. Even though the PQ symmetry was at its origin, duality is nevertheless {\it not} broken by this effect. Below condensation scale, the axion simply gets a mass, but in the `stringy' version, the $ B_{μν}$ field disappears from the propagating spectrum. Its place is taken by a massive 3-index antisymmetric field $H_{μνρ}$ which is the one dual to the massive axion. This is a particular case of a ge…
We argue that in the tensionless phase of string theory where the stringy gauge symmetries are unbroken, (at least some) cosmological singularities can be understood as gauge artefacts. We present two conceptually related, but distinct, pieces of evidence: one relying on spacetime and the other on worldsheet.
We construct a bi-linear form on the periods of Calabi-Yau spaces. These are used to obtain the prepotentials around conifold singularities in type-II strings compactified on Calabi-Yau space. The explicit construction of the bi-linear forms is achieved for the one-moduli models as well as two moduli models with K3-fibrations where the enhanced gauge symmetry is known to be observed at conifold locus. We also show how these bi-linear forms are related with the existence of flat coordinates. We list the resulting prepotentials in two moduli models around the conifold locus, which contains alpha…
Generically, string models with $N=1$ supersymmetry are not expected to have moduli beyond perturbation theory; stringy non-perturbative effects as well as low energy field-theoretic phenomena such as gluino condensation will lift any flat directions. In this note, we describe models where some subspace of the moduli space survives non-perturbatively. Discrete $R$ symmetries forbid any inherently stringy effects, and dynamical considerations control the field-theoretic effects. The surviving subspace is a space of high symmetry; the system is attracted to this subspace by a potential which we …
We propose a scenario of gauge-string correspondence by relating the SU(3) colour group to hidden space-time isometries originating from extra dimensions. These isometries ($α$-symmetries) are the special symmetries of RNS superstring theories under global non-linear space-time transformations. The vertex operators for the octet of gluons are constructed by the procedure of ``photon painting'', that is, with the SU(3) subgroup of the $α$-symmetry generators acting on a regular open string photon, so the corresponding open string excitations are in the adjoint of SU(3). Remarkably, the operator…
The focus of the present thesis is on the analysis of gauge symmetry and its various impacts on gauge theories. In the first part of this thesis, we have studied different aspects of symmetries in connection with various field and string theoretic models. The manifestations of gauge symmetries and their interconnection with the diffeomorphism invariances have been discussed in the context of different generally covariant models like string, membrane, $p-$brane and metric gravity. Analysis of interacting string with proper inclusion of the stringy boundary conditions led to the noncommutative n…
In this dissertation we study hidden symmetries within the framework of string theory. There are two kinds of hidden symmetries investigated in this work: the first type is associated with dynamics of quantum fields and the second type is related to integrability of strings on various backgrounds. The goals of this thesis are twofold: extension of hidden symmetries known in general relativity to stringy backgrounds in higher dimensions and construction of new integrable string theories. In the context of the first goal we study hidden symmetries of stringy backgrounds, with and without supersy…
We overview symmetries of string scattering amplitudes in the high energy limits of both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated high energy string scattering amplitudes (SSA) at arbitrary mass levels for both regimes. We discovered the infinite linear relations among fixed angle string amplitudes and the infinite recurrence relations among Regge string amplitudes. The linear relations we obtained in the GR corrected the saddle point calculations by Gross, Gross and Mende. In addition, for the high energy closed string scattering…
We derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action to first order in alpha prime using Wald's formalism. We carefully take into account all the symmetries of the theory and, as a result, we obtain a manifestly gauge- and Lorentz-invariant entropy formula in which all the terms can be computed explicitly. An entropy formula with these properties allows unambiguous calculations of macroscopic black-hole entropies to first order in alpha prime that can be reliably used in a comparison with the microscopic ones. Such a formula was still lac…
Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Zn gauge symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete `stringy' Zn symmetries are trivial from the field theory point of view, while others have not been id…
This paper tentatively conjectures a possible physical picture that may help explain links between quantum field theories and string theories. A correspondence might occur if the stringy parameters $τ$ and $σ_i $ are interpreted as representing particular types of observer capabilities. Observer limitations could be imposed by symmetries of relevant quantum mechanical observer states. It is possible that this postulate may in future be able to go a small way towards understanding a physical basis for some of the dualities that have been found in string/field theory.
We propose a variation of spacetime noncommutative field theory to realize the stringy spacetime uncertainty relation without breaking any of the global symmetries of the homogeneous isotropic universe. We study the spectrum of metric perturbations in this model for a wide class of accelerating background cosmologies. Spacetime noncommutativity leads to a coupling between the fluctuation modes and the background cosmology which is nonlocal in time. For each mode, there is a critical time at which the spacetime uncertainty relation is saturated. This is the time when the mode is generated. Thes…
We re-derive the first law of black hole mechanics in the context of the Heterotic Superstring effective action compactified on a torus to leading order in alpha prime, using Wald's formalism, covariant Lie derivatives and momentum maps. The Kalb-Ramond field strength of this theory has Abelian Chern-Simons terms which induce Nicolai-Townsend transformations of the Kalb-Ramond field. We show how to deal with all these gauge symmetries deriving the first law in terms of manifestly gauge-invariant quantities. In presence of Chern-Simons terms, several definitions of the conserved charges exist, …
We point out that the moduli sector of the $(2,2)$ string compactification with its nonperturbatively preserved non-compact symmetries is a fertile framework to study global topological defects, thus providing a natural source for the large scale structure formation. Based on the target space modular invariance of the nonperturbative superpotential of the four-dimensional N=1 supersymmetric string vacua, topologically stable stringy domain walls are found. They are supersymmetric solutions, thus saturating the Bogomolnyi bound. It is also shown that there are moduli sectors that allow for the …
Double Field Theory suggests to view the whole massless sector of closed strings as the gravitational unity. The fundamental symmetries therein, including the $\mathbf{O}(D,D)$ covariance, can determine unambiguously how the Standard Model as well as a relativistic point particle should couple to the closed string massless sector. The theory also refines the notion of singularity. We consider the most general, spherically symmetric, asymptotically flat, static vacuum solution to ${D=4}$ Double Field Theory, which contains three free parameters and consequently generalizes the Schwarzschild geo…
Modular transformations of string theory (including the well-known stringy dualities) play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They are at the origin of CP transformations and provide a unification of CP with traditional flavor symmetries. Here, we present a novel, fully systematic method to reliably compute the unified flavor symmetry of the low-energy effective theory, including enhancements from the modular transformations of string theory. The unified flavor group is non-universal in moduli space and exhibits the phenomenon of "Local Flavor…
We show that, without any extra physical degree introduced, the Standard Model can be readily reformulated as a Double Field Theory. Consequently, the Standard Model can couple to an arbitrary stringy gravitational background in an $\mathbf{O}(4,4)$ T-duality covariant manner and manifest two independent local Lorentz symmetries, $\mathbf{Spin}(1,3)\times\mathbf{Spin}(3,1)$. While the diagonal gauge fixing of the twofold spin groups leads to the conventional formulation on the flat Minkowskian background, the enhanced symmetry makes the Standard Model more rigid, and also stringy, than it appe…
The soft bootstrap is an on-shell method to constrain the landscape of effective field theories (EFTs) of massless particles via the consistency of the low-energy S-matrix. Given assumptions on the on-shell data (particle spectra, linear symmetries, and low-energy theorems), the soft bootstrap is an efficient algorithm for determining the possible consistency of an EFT with those properties. The implementation of the soft bootstrap uses the recently discovered method of soft subtracted recursion. We derive a precise criterion for the validity of these recursion relations and show that they fai…
The scattering equation formalism for scattering amplitudes, and its stringy incarnation, the ambitwistor string, remains a mysterious construction. In this paper, we pursue the study a gauged-unfixed version of the ambitwistor string known as the null string. We explore the following three aspects in detail; its complexification, gauge fixing, and amplitudes. We first study the complexification of the string; the associated symmetries and moduli, and connection to the ambitwistor string. We then look in more details at the leftover symmetry algebra of the string, called Galilean conformal alg…
It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS3 x S3 x T4. At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the N=4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS3, indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of…
The temperature of the chiral restoration phase transition at 130 MeV as well as the temperature of the center symmetry ("deconfinement") phase transition in a pure glue theory at 300 MeV are two independent temperatures and their interplay determines a structure of different regimes of hot QCD. Given a chiral spin symmetry of the color charge and of the chromoelectric interaction we can conclude from observed symmetries of spatial and temporal correlators of N_F=2 QCD with domain wall Dirac operator at physical quark masses that above the chiral symmetry restoration crossover around T_pc but …
We study n-point tree amplitudes of N=4 super Yang-Mills theory and N=8 supergravity for general configurations of external particles of the two theories. We construct generating functions for n-point MHV and NMHV amplitudes with general external states. Amplitudes derived from them obey SUSY Ward identities, and the generating functions characterize and count amplitudes in the MHV and NMHV sectors. The MHV generating function provides an efficient way to perform the intermediate state helicity sums required to obtain loop amplitudes from trees. The NMHV generating functions rely on the MHV-ve…
We review how D-brane instantons can generate open string couplings of stringy hierarchy in the superpotential which violate global abelian symmetries and are therefore perturbatively forbidden. We discuss the main ingredients of this mechanism, focussing for concreteness on Euclidean $D2$-branes in Type IIA orientifold compactifications. Special emphasis is put on a careful analysis of instanton zero modes and a classification of situations leading to superpotential or higher fermionic F-terms. This includes the discussion of chiral and non-chiral instanton recombination, viewed as a multi-in…
In contrast to the common wisdom, we discover that, instead of the exponential fall-off of the form factors with Regge-pole structure, the high-energy scattering amplitudes of string scattered from Domain-wall behave as power-law with Regge-pole structure. This is to be compared with the well-known power-law form factors without Regge-pole structure of the D-instanton scatterings. This discovery makes Domain-wall scatterings an unique example of a hybrid of string and field theory scatterings. The calculation is done for bosonic string scatterings of arbitrary massive string states from D-24 b…
There exists a widely spread notion that gravitational effects can strongly violate global symmetries. It may lead to many important consequences. We will argue, in particular, that nonperturbative gravitational effects in the axion theory lead to a strong violation of CP invariance unless they are suppressed by an extremely small factor 10^{-82}. One could hope that this problem disappears if one represents the global symmetry of a pseudoscalar axion field as a gauge symmetry of the Ogievetsky-Polubarinov-Kalb-Ramond antisymmetric tensor field. We will show, however, that this gauge symmetry …
We review high energy symmetries of string theory at both the fixed angle or Gross regime (GR) and the fixed momentum transfer or Regge regime (RR). We calculated in details high energy string scattering amplitudes at arbitrary mass levels for both regimes. We discovered infinite linear relations among fixed angle string amplitudes conjectured by Gross in 1988 from decoupling of high energy zero-norm states (ZNS), and infinite recurrence relations among Regge string amplitudes from Kummer function U and Appell function F_1. However, the linear relations we obtained in the GR corrected [27-32] …
We show that the BMN operators in D=4 N=4 super Yang Mills theory proposed as duals of stringy oscillators in a plane wave background have a natural quantum group construction in terms of the quantum deformation of the SO(6) $R$ symmetry. We describe in detail how a q-deformed U(2) subalgebra generates BMN operators, with $ q \sim e^{2 i π\over J}$. The standard quantum co-product as well as generalized traces which use $q$-cyclic operators acting on tensor products of Higgs fields are the ingredients in this construction. They generate the oscillators with the correct (undeformed) permutation…
