Davide Forcella, Amihay Hanany, Jan Troost
We provide generating functions for the perturbative massive string spectrum which are covariant with respect to the SO(9) little group, and which contain all the representation theoretic content of the spectrum. Generating functions for perturbative bosonic, Type II, Heterotic and Type I string theories are presented, and generalizations are discussed.
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We give a gauge and manifestly SO(2,2) covariant formulation of the field theory of the self-dual string. The string fields are gauge connections that turn the super-Virasoro generators into covariant derivatives.
Within the framework of the Covariant formulation of Light-Front Dynamics, we develop a general non-perturbative renormalization scheme, based on the Fock decomposition of the state vector and its truncation. The explicit dependence of our formalism on the orientation of the light front, defined by a light-like four vector $ω$, is essential in order to analyze the structure of the counterterms needed to renormalize the theory. We illustrate our framework for scalar and fermion models
We point out the existence of a non-perturbative exact nilpotent BRST symmetry for the Gribov-Zwanziger action in the Landau gauge. We then put forward a manifestly BRST invariant resolution of the Gribov gauge fixing ambiguity in the linear covariant gauge.
In this short note we formulate Covariant Hamiltonian formalism for strings, p-branes and Non-BPS Dp-branes. We also analyse the vacuum tachyon condensation in case of unstable D1-brane.
The quantum algebra of observables of the massive closed bosonic string in 1+3 dimensions has been developed so far in the rest frame of the string. In this paper a method to write this algebra in a manifestly Lorentz covariant form is explained and compared with an alternative approach in the literature.
We study covariant open bosonic string field theories on multiple $Dp$-branes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple $Dp$-branes, we obtain the field theoretical effective action in the zero-slope limit. On the multiple $D0$-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between the open string field theory on multiple $D$-insta…
A single-parameter family of covariant gauge fixing conditions in bosonic string field theory is proposed. It is a natural string field counterpart of the covariant gauge in the conventional gauge theory, which includes the Landau gauge as well as the Feynman (Siegel) gauge as special cases. The action in the Landau gauge is largely simplified in such a way that numerous component fields have no derivatives in their kinetic terms and appear in at most quadratic in the vertex.
S-matrices can be written Lorentz covariantly in terms of free field strengths for vector states, allowing arbitrary gauge choices. In string theory the vertex operators can be chosen so this gauge invariance is automatic. As examples we give four-vector (super)string tree amplitudes in this form, and find the field theory actions that give the first three orders in the slope.
Operator nucleon vertices are constructed in composite superconformal string model. Splitting of baryon Regge trajectories with the same quantum numbers but with opposite parity is provided by inclusion of simple additional components to superconformal generators.
We discuss the integrability of the Berkovits-Siegel open string field equations and derive an infinite set of their non-local (solution-generating) symmetries. The string field equations are embedded in an infinite system of overdetermined equations (BS hierarchy) associated with hidden string symmetries. The latter enforce the vanishing of most scattering amplitudes for the open N=2 string.
Causality is studied in the covariant formulation of free string field theory (SFT). We find that, though the string field in the covariant formulation is a functional of the ghost coordinates as well as the space-time coordinate and the latter contains the time-like oscillators with negative norm, the condition for the commutator of two open string fields to vanish is simply given by $\int_0^πdσ\left(ΔX^μ(σ)\right)^2 >0$, which is the same condition as in the light-cone gauge SFT. For closed SFT, the corresponding condition is given in a form which is manifestly invariant under the rigid shif…
We present a construction of string--localized covariant free quantum fields for a large class of irreducible (ray) representations of the Poincare group. Among these are the representations of mass zero and infinite spin, which are known to be incompatible with point-like localized fields. (Based on joint work with B.Schroer and J.Yngvason [13].)
The covariant quantization of the tensionless free bosonic (open and closed) strings in AdS spaces is obtained. This is done by representing the AdS space as an hyperboloid in a flat auxiliary space and by studying the resulting string constrained hamiltonian system in the tensionless limit. It turns out that the constraint algebra simplifies in the tensionless case in such a way that the closed BRST quantization can be formulated and the theory admits then an explicit covariant quantization scheme. This holds for any value of the dimension of the AdS space.
The recently discovered $O(d,d)$ symmetry of the space of slowly varying cosmological string vacua in $d+1$ dimensions is shown to be preserved in the presence of bulk string matter. The existence of $O(d,d)$ conserved currents allows all the equations of string cosmology to be reduced to first-order differential equations. The perfect-fluid approximation is not $O(d,d)$-invariant, implying that stringy fluids possess in general a non-vanishing viscosity.
We derive boundary conditions for the covariant open string corresponding to D-branes in an Hpp-wave, by requiring kappa symmetry of its bulk action. Both half-supersymmetric and quarter-supersymmetric branes are seen to arise in this way, and the analysis furthermore agrees fully with the existing probe brane and supergravity computations. We elaborate on the origin of dynamical and kinematical supersymmetries from the covariant point of view. In particular we focus on the D-string which only preserves half of the dynamical supersymmetries and none of the kinematical ones. We discuss its orig…
A general family of charge-current carrying cosmic string models is investigated. In the special case of circular configurations in arbitrary axially symmetric gravitational and electromagnetic backgrounds the dynamics is determined by simple point particle Hamiltonians. A certain "duality" transformation relates our results to previous ones, obtained by Carter et. al., for an infinitely long open stationary string in an arbitrary stationary background.
We present the covariant BRST quantization of the super-D-string. The non-vanishing supersymmetric U(1) field strength ${\cal F}$ is essential for the covariant quantization of the super-D-string as well as for its static picture. A SO(2) parameter parametrizes a family of local supersymmetric (kappa symmetric) systems including the super-D-string with ${\cal F}\ne 0$ and the Green-Schwarz superstring with ${\cal F}= 0$. We suggest that $E^1$ (canonical conjugate of U(1) gauge field) plays a role of the order parameter in the Green-Schwarz formalism: the super-D-string exists for $E^1 \ne 0$ w…
Yang-Mills theories at finite temperature quantized in linear covariant gauges: gauge copies and semi-non-perturbative effects
该研究针对有限温度下最大阿贝尔规范和线性协变规范中量子化的四维欧几里得杨-米尔斯理论，通过混合方法探索有限温度效应与移除格里博副本的相互作用，验证了胶子自由度的三种相。
Duality covariant curvature and torsion tensors in double field theory/generalized geometry are central in analyzing consistent truncations, generalized dualities, and related integrable $σ$-models. They are constructed systematically with the help of a larger, auxiliary space in a procedure inspired by Cartan geometry originally proposed by Poláček and Siegel for bosonic strings. It pivots around a maximally isotropic group that captures the generalized structure group of the physical space. We show how dropping the isotropy condition on this group allows us to describe heterotic/type I strin…
The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative construction of renormalized interacting models on generic curved backgrounds and opens in principle the way towards a background independent perturbative quantization of gravity.
A systematic scheme is developed for solving conformal algebra of the massive vertex operators in the old covariant first quantized string theory. Using the first massive level in the covariant spectrum of bosonic open string theory in flat space-time as an example, we explicitly verify the conformal algebra for the normal-ordered covariant vertex operator. We emphasize that the requirement of fully covariant gauge-fixing specifies the form of normal-ordering for massive vertex operators.
In this paper we discuss two approaches to anomaly-free quantization of a two-dimensional string. The first approach is based on the canonical Dirac prescription of quantization of degenerated systems. At the second approach we "weaken" the Dirac quantization conditions requiring the solving of first class constraints only in the sense of mean values. At both approaches there are no states with the indefinite metrics.
The main goal of this paper is the manifestly covariant derivation of the classical relation between the gauge-fixed Grassmann variables of the NSR string and the Type II GS superstring. To this end we analyze the superembedding equation for the Type II superstring to derive the relation between the original variables of the NSR string and the Type II GS superstring and, further, by means of Lorentz harmonic variables we fix $κ-$symmetry of the GS superstring in the manifestly Lorentz covariant way.
We address the issue of the worldsheet and spacetime covariant formulation for matrix strings. The problem is solved in the limit of vanishing string coupling. To go beyond the g_s = 0 limit, we propose a topological quantum field theory as a twisted candidate. Our model involves the generalized octonionic or SU(4) instanton equations defined in eight dimensions for a supersymmetric U(N) Yang--Mills field living on a special holonomy manifold. The question of untwisting this matrix model into an anomaly free theory enlightens the need for an "extended" 2d-gravity sector, that we suggest could …
The gauge invariant loop variable formalism and old covariant formalism for bosonic open string theory are compared in this paper. It is expected that for the free theory, after gauge fixing, the loop variable fields can be mapped to those of the old covariant formalism in bosonic string theory, level by level. This is verified explicitly for the first two massive levels. It is shown that (in the critical dimension) the fields, constraints and gauge transformations can all be mapped from one to the other. Assuming this continues at all levels one can give general arguments that the tree S-matr…
We investigate the variation of the string field action under changes of the string field vertices giving rise to different decompositions of the moduli spaces of Riemann surfaces. We establish that any such change in the string action arises from a field transformation canonical with respect to the Batalin-Vilkovisky (BV) antibracket, and find the explicit form of the generator of the infinitesimal transformations. Two theories using different decompositions of moduli space are shown to yield the same gauge fixed action upon use of different gauge fixing conditions. We also elaborate on recen…
We construct a covariant formulation of the heterotic superstring on K3 times T^2 with manifest N=2 supersymmetry. We show how projective superspace appears naturally in the hybrid formulation giving a (partially) geometric interpretation of the harmonic parameter. The low-energy effective action for this theory is given by a non-standard form of N=2 supergravity which is intimately related to the N=1 old-minimal formulation. This formalism can be used to derive new descriptions of interacting projective superspace field theories using Berkovits' open string field theory and the the heterotic …
A general formalism for covariant $W_3$ string scattering is given. It is found necessary to use screening charges that are constructed from the $W_3$ fields including ghosts. The scattering amplitudes so constructed contain within them Ising model correlation functions and agree with those found previously by the authors. Using the screening charge and a picture changing operator, an infinite number of states in the cohomology of Q are generated from only three states. We conjecture that, apart from discrete states, these are all the states in the cohomology of Q.
We discuss a covariant functional integral approach to the quantization of the bosonic string. In contrast to approaches relying on non-covariant operator regularizations, interesting operators here are true tensor objects with classical transformation laws, even on target spaces where the theory has a Weyl anomaly. Since no implicit non-covariant gauge choices are involved in the definition of the operators, the anomaly is clearly separated from the issue of operator renormalization and can be understood in isolation, instead of infecting the latter as in other approaches. Our method is of wi…
This paper is a shortened version of the previous work hep-th/9907099: We propose a topological quantum field theory as a twisted candidate to formulate covariant matrix strings. The model relies on the octonionic or complexified instanton equations defined on an eight dimensional manifold with reduced holonomy. To allow untwisting of the model without producing an anomaly, we suggest (partially twisted) W-gravity as an "extended" 2d-gravity sector.
We construct a covariant open bosonic string field theory on multiple D-branes, which reduces to a non-Abelian group Yang-Mills gauge theory in the zero-slope limit. Making use of the first quantized open bosonic string in the proper time gauge, we convert the string amplitudes given by the Polyakov path integrals on string world sheets into those of the second quantized theory. The world sheet diagrams generated by the constructed open string field theory are planar in contrast to those of the Witten's cubic string field theory. However, the constructed string field theory is yet equivalent t…
We analyze a recent conjecture regarding the perturbative construction of non-linear deformations of all classically duality invariant theories, including N=8 supergravity. Starting with an initial quartic deformation, we engineer a procedure that generates a particular non-linear deformation (Born-Infeld) of the Maxwell theory. This procedure requires the introduction of an infinite number of modifications to a constraint which eliminates degrees of freedom consistent with the duality and field content of the system. We discuss the extension of this procedure to N=1 and N=2 supersymmetric the…
It is shown that the idea of ``minimal'' coupling to gauge fields can be conveniently implemented in the proper time formalism by identifying the equivalent of a ``covariant derivative''. This captures some of the geometric notion of the gauge field as a connection. The proper time equation is also generalized so that the gauge invariances associated with higher spin massive modes can be made manifest, at the free level, using loop variables. Some explicit examples are worked out illustrating these ideas.
The reduced covariant phase space associated with the three-dimensional Euclidean Nambu-Goto action can be identified, via the Enneper-Weierstrass representation of minimal surfaces, with the space of complex analytic functions plus three translational zero modes. The symplectic structure induced trough the Enneper-Weierstrass map can be explicitly computed. Quantization is then straightforward, yielding as a result a target-space Euclidean-invariant, positive-definite, two-dimensional quantum field theory. The physical states are shown to correspond with particles states of integer spin and a…
By considering the superembedding equation for the Type II superstring we derive the classical relation between the NSR string and the Type II GS superstring Grassmannian variables. The connection between the actions of these two models is also established. Then introducing the proper twistor-like Lorentz harmonic variables we fix $κ-$symmetry of the GS formulation in the manifestly SO(1,9) Lorentz covariant manner and establish the relation between the gauge-fixed variables of the NSR and the Type II GS models.
A note on gauge-covariant vertex operators of the ambitwistor string
本文在玻色子ambitwistor弦中构造规范协变顶点算符，通过反鬼场无关子复形实现无洛伦兹条件的BRST闭包，并区分于完整相对BRST上同调。
The covariant canonical method of quantization based on the De Donder-Weyl covariant canonical formalism is used to formulate a world-sheet covariant quantization of bosonic strings. To provide the consistency with the standard non-covariant canonical quantization, it is necessary to adopt a Bohmian deterministic hidden-variable equation of motion. In this way, string theory suggests a solution to the problem of measurement in quantum mechanics.
I introduced the quadratic gauge for $SU(N)$ Yang-Mills theory and demonstrated its substantial implications in the non-perturbative theory in my previous works. An interesting case is to understand its implications in a perturbative regime and ask whether they differ anyway from the well established theory in this regime. Here I aim to calculate the beta function at one loop level in the same gauge.
We rewrite the SL(2,Z) covariant worldsheet action for the IIB string proposed by Townsend in a Polyakov form. In a flat background the formalism yields separate (p,q) sectors. In each one the action is that of the IIB string action with the string slope parameter \alp\pr replaced by its SL(2,Z) analogue \alp_{pq}\pr. SL(2,Z) invariant graviton scattering amplitudes are obtained from those of the fundamental (1,0) string by summing over the different sectors. The tree-level four-graviton amplitude in this formalism differs from a previously conjectured non-perturbative form; both yield the sam…
We show that a-gauge, a class of covariant gauges developed for bosonic open string field theory, is consistently applied to the closed string field theory. A covariantly gauge-fixed action of massless fields can be systematically derived from a-gauge-fixed action of string field theory.
Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessaary for a consistent computation of the en…
The section condition in double field theory has been shown to imply that a physical point should be one-to-one identified with a gauge orbit in the doubled coordinate space. Here we show the converse is also true, and continue to explore the idea of `spacetime being doubled yet gauged'. Introducing an appropriate gauge connection, we construct a string action, with an arbitrary generalized metric, which is completely covariant with respect to the coordinate gauge symmetry, generalized diffeomorphisms, world-sheet diffeomorphisms, world-sheet Weyl symmetry and O(D,D) T-duality. A topological t…
In this paper we summarize our recent work about perturbative and non-perturbative effects in four-dimensional heterotic strings with $N=2$ space-time supersymmetry.
Covariant Closed String Bits -- Classical Theory
本文研究了描述束缚弦比特自由运动的连续时间格点世界面理论，利用非局域格点导数保留连续统对称性，建立局域对应关系，并在格点上验证了全局对称性代数与经典Virasoro代数，可推广至高维广义协变理论。
These lectures provide an introduction to perturbative string theory and its construction on spaces with background Ramond flux. Traditional covariant quantization of the string and its connection with vertex operators and conformal invariance of the worldsheet theory are reviewed. A supersymmetric covariant quantization of the superstring in six and ten spacetime dimensions is discussed. Correlation functions are computed with these variables. Applications to strings in anti-de Sitter backgrounds with Ramond flux are analyzed. Based on lectures presented at the Theoretical Advanced Study Inst…
A covariant calculus for the construction of effective string theories is developed. Effective string theory, describing quantum string-like excitations in arbitrary dimension, has in the past been constructed using the principles of conformal field theory, but not in a systematic way. Using the freedom of choice of field definition, a particular field definition is made in a systematic way to allow an explicit construction of effective string theories with manifest exact conformal symmetry. The impossibility of a manifestly invariant description of the Polchinski-Strominger Lagrangian is demo…
New non-perturbative interactions in the effective action of two dimensional string theory are described. These interactions are due to ``stringy" instantons
We construct a covariant generating function for the spectrum of chiral primaries of symmetric orbifold conformal field theories with N=(4,4) supersymmetry in two dimensions. For seed target spaces K3 and T4, the generating functions capture the SO(21) and SO(5) representation theoretic content of the chiral ring respectively. Via string dualities, we relate the transformation properties of the chiral ring under these isometries of the moduli space to the Lorentz covariance of perturbative string partition functions in flat space.
We consider quantum N=2 string embedded into the N=4 topological framework from the perspective of the old covariant quantisation. Making use of the causality and cyclic symmetry of tree amplitudes we argue that no Lorentz covariant boson emission vertex can be constructed within the N=4 topological formalism.
The propagators of the Faddeev-Popov (FP) ghosts for Yang-Mills theories and perturbative quantum gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. We point out, however, that the modes responsible for these divergences will not contribute to loop diagrams in computations of time-ordered products in either Yang-Mills theories or perturbative quantum gravity. Therefore we propose that the IR divergent FP-ghost propagator should be regularized by a small mass term that is sent to zero in the end of any perturbative calculations. This proposal is equivalent to usi…
We use a combination of a 't Hooft limit and numerical methods to find non-perturbative solutions of exactly solvable string theories, showing that perturbative solutions in different asymptotic regimes are connected by smooth interpolating functions. Our earlier perturbative work showed that a large class of minimal string theories arise as special limits of a Painleve IV hierarchy of string equations that can be derived by a similarity reduction of the dispersive water wave hierarchy of differential equations. The hierarchy of string equations contains new perturbative solutions, some of whi…
These are a set of lectures presented at the CERN-La Plata-Santiago de Compostella School of Physics, La Plata, May 1997. A brief introduction to the non-perturbative structure of string theory is presented. Various non-perturbative dualities in ten and six dimensions as well as D-branes are discussed.
We examine how to construct explicit heterotic string models dual to F-theory in eight dimensions. In doing so we learn about where the moduli spaces of the two theories overlap, and how non-perturbative features leave traces on a purely perturbative level. We also propose a modified T-duality linking M and F-theories based on non-perturbative structures of string theories in eight dimensions.
In this talk we summarise our recent results on perturbative and non-perturbative monodromies in four-dimensional heterotic strings with $N=2$ space-time supersymmetry, and we compare our results with the rigid $SU(2)$ $N=2$ Yang-Mills monodromies.
We canonically quantize closed string theory in the pp-wave background with a non-zero flux of the three-form field strength by using the covariant BRST operator formalism. In this canonical quantization, we completely construct new covariant free-mode representations, for which it is particularly important to take account of the commutation relations of the zero mode of the light-cone string coordinate X^{-} with other modes. All covariant string coordinates are composed of the free-modes. Moreover, employing these covariant string coordinates for the energy-momentum tensor, we calculate the …
We give the first construction of covariant coherent closed string states, which may be identified with fundamental cosmic strings. We outline the requirements for a string state to describe a cosmic string, and using DDF operators provide an explicit and simple map that relates three different descriptions: classical strings, lightcone gauge quantum states and covariant vertex operators. The naive construction leads to covariant vertex operators whose existence requires a lightlike compactification of spacetime. When the lightlike compactified states in the underlying Hilbert space are projec…
We make a simple observation that the massless continuous spin representations of the Poincaré group are not present in perturbative string theory constructions. This represents one of the very few model-independent low-energy consequences of these models.
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 results 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 interpret…
The perturbative dynamics of noncommutative field theory (NCFT) is discussed from a point view of string field theory. As in the commutative case it is inevitable to introduce a closed string, which may be described as a bound state of two noncommutative open strings. We point out that the closed string, interacting nontrivially with the open string, plays an essential role in the ultraviolet region. The contribution of the closed string is responsible for the discrepancy between the NCFT and the string field theory. It clarifies the controversial issues associated with the ultraviolet/infrare…
The conjecture that M-theory has the rank eleven Kac-Moody symmetry e11 implies that Type IIA and Type IIB string theories in ten dimensions possess certain infinite dimensional perturbative symmetry algebras that we determine. This prediction is compared with the symmetry algebras that can be constructed in perturbative string theory, using the closed string analogues of the DDF operators. Within the limitations of this construction close agreement is found. We also perform the analogous analysis for the case of the closed bosonic string.
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