String center of mass operator and its effect on BRST cohomology

We consider the theory of bosonic closed strings on the flat background ℝ^25,1. We show how the BRST complex can be extended to a complex where the string center of mass operator,x ₀ ^μ is well defined. We investigate the cohomology of the extended complex. We demonstrate that this cohomology has a number of interesting features. Unlike in the standard BRST cohomology, there is no doubling of physical states in the extended complex. The cohomology of the extended complex is more physical in a number of aspects related to the zero-momentum states. In particular, we show that the ghost number one zero-momentum cohomology states are in one to one correspondence with the generators of the global symmetries of the backgroundi.e., the Poincaré algebra. Supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative agreement #DF-FC02-94ER40818     

Field theory of interacting open superstrings in fermionic ghost representation

The field theory of interacting open superstring in the fermionic ghost representation based on anticommuting and commuting ghosts, corresponding respectively to world sheet bosonic x_μ and fermionic ψ_μ coordinates, is presented. We have to revise once more the field theory of the free Ramond (R) string and starting from a general algebraic point of view we obtain that the number of degrees of freedom in the R and NS (Neveu-Schwarz) sectors are equal, permitting us to construct a supersymmetric operator. We propose to solve a specific equation guaranteeing superinvariance in order to find the R-R-NS and NS-R-R vertices in the term of the NS-NS-NS vertex.     

Refined Chiral Slavnov–Taylor Identities: Renormalization and Local Physics

We study the quantization of chiral QED with one family of massless fermions and the Stueckelberg field in order to give mass to the Abelian gauge field in a BRST-invariant way. We show that an extended Slavnov–Taylor (ST) identity can be introduced and fulfilled to all orders in perturbation theory by a suitable choice of the local actionlike counterterms, order by order in the loopwise expansion. This ST identity incorporates the Adler–Bardeen anomaly and involves the introduction of a doublet (K, c), where K is an external source of dimension 0 and c is the ghost field. By a purely algebraic argument we show that the introduction of the source K trivializes the cohomology of the extended linearized classical ST operator S ₀ in the Fadeev–Popov (FP) charge + 1 sector.We discuss the physical content of the extended ST identity and prove that the cohomology classes associated with S ₀ are modified with respect to the ones of the classical BRST differential s in the FP neutral sector (physical observables). This provides a counterexample showing that the introduction of a doublet can modify the cohomology of the model, as a consequence of the fact that the counting operator for the doublet (K, c) does not commute with S ₀ .We explicitly check that the physical states defined by s are no more physical states of the full quantized theory by showing that the subspace of the physical states corresponding to s is not left-invariant under the application of the S matrix, as a consequence of the extended ST identity.     

Chiral BRST Cohomology of N= 2 Strings at Arbitrary Ghost and Picture Number

We compute the BRST cohomology of the holomorphic part of the N= 1 string at arbitrary ghost and picture number. We confirm the expectation that the relative cohomology at non-zero momentum consists of a single massless state in each picture. The absolute cohomology is obtained by an independent method based on homological algebra. For vanishing momentum, the relative and absolute cohomologies both display a picture dependence – a phenomenon discovered recently also in the relative Ramond sector of N= 1 strings by Berkovits and Zwiebach [1]. Received: 5 January 1998 / Accepted: 16 November 1998     

The gauging of BV algebras

A BV algebra is a formal framework within which the BV quantization algorithm is implemented. In addition to the gauge symmetry, encoded in the BV master equation, the master action often exhibits further global symmetries, which may be in turn gauged. We show how to carry this out in a BV algebraic set up. Depending on the nature of the global symmetry, the gauging involves coupling to a pure ghost system with a varying amount of ghostly supersymmetry. Coupling to an N=0$N=0$ ghost system yields an ordinary gauge theory whose observables are appropriately classified by the invariant BV cohomology. Coupling to an N=1$N=1$ ghost system leads to a topological gauge field theory whose observables are classified by the equivariant BV cohomology. Coupling to higher N$N$ ghost systems yields topological gauge field theories with higher topological symmetry. In the latter case, however, problems of a completely new kind emerge, which call for a revision of the standard BV algebraic framework.     

Central peak for a scalar ϕ 4-model: mode coupling approach revisited

We reinvestigate the mode coupling approach to the central peak which occurs in the vicinity of a structural phase transition at T _c. For a scalar ? ⁴-model it is shown that the use of renormalized vertices leads to quite different results compared to recent calculations with bare vertices. Particularly, we prove that the latter are obtained in leading order of the anharmonicity constant of the on-site potential from a perturbational treatment of the renormalized vertices. Again, this mode coupling approach may yield a dynamical transition at a temperature T _c'(≥ T _c) at which the dynamics becomes nonergodic, i.e. a central peak occurs. For a ? ⁴- model with infinite range interactions our theoretical predictions are consistent with numerical results. Furthermore, if the fluctuations in the vicinity of Tc are Gaussian, no dynamical transition occurs above Tc. Therefore the temperature T ₀'obtained from the Ginzburg criterion sets an upper bound for T _c'. If a dynamical transition occurs, it is shown that the nonergodicity parameter as function of wave vector q and temperature T follows from an universal master function.     

On the classical dynamics of a pure spinor string on an AdS5×S5 background

We will discuss some properties of the pure spinor string on an AdS₅×S⁵ background. Using a classical Hamiltonian analysis we will show that the vertex operator for the massless state that is in the cohomology of the BRST charges describes on-shell fluctuations around an AdS₅×S⁵ background.     

Laplace operator and hodge decomposition for quantum groups and quantum spaces

LetΓ=Γ _±,z be one of theN ²-dimensional bicovariant first order differential calculi for the quantum groups GL _q (N), SL _q (N), SO _q (N), or Sp _q (N), whereq is a transcendental complex number andz is a regular parameter. It is shown that the de Rham cohomology of Woronowicz’s external algebraΓ ^{^} coincides with the de Rham cohomologies of its leftinvariant, its right-invariant and its biinvariant subcomplexes. In the cases GL _q (N) and SL _q (N) the cohomology ring is isomorphic to the biinvariant external algebraΓ _inv ^{^} and to the vector space of harmonic forms. We prove a Hodge decomposition theorem in these cases. The main technical tool is the spectral decomposition of the quantum Laplace-Beltrami operator. It is also applicable for quantum Euclidean spheres. The eigenvalues of the Laplace-Beltrami operator in cases of the general linear quantum group, the orthogonal quantum group, and the quantum Euclidean spheres are given.     

Type IIB string theory on AdS5×T

We study Kaluza-Klein spectrum of type IIB string theory compactified on AdS₅×T^nn′ in the context of AdS/CFT correspondence. We examine some of the modes of the complexified 2 form potential as an example and show that for the states at the bottom of the Kaluza-Klein tower the corresponding d=4 boundary field operators have rational conformal dimensions. The masses of some of the fermionic modes in the bottom of each tower as functions of the R charge in the boundary conformal theory are also rational. Furthermore the modes in the bottom of the towers originating from q forms on T¹¹ can be put in correspondence with the BRS cohomology classes of the c=1 non critical string theory with ghost number q.     

A Module Structure on the Symplectic Floer Cohomology

The aim of this paper is to offer an affirmative answer to the Floer conjectures in [2, p. 589] which states that there is a module structure on the Z _{2 N} -graded symplectic Floer cohomology for monotone symplectic manifolds. By constructing a Z-graded symplectic Floer cohomology as an integral lift of the Z _{2 N} -graded symplectic Floer cohomology, we gain control of the holomorphic bubbling spheres. This makes a module structure on the Z-graded Floer cohomology. There is a spectral sequence with E ¹ _*,* given by the Z-graded symplectic Floer cohomology. Such a spectral sequence converges to the Z _{2 N} -graded symplectic Floer cohomology. Hence we induce a module structure for the Z _{2 N} -graded symplectic Floer cohomology by the spectral sequence and algebraic topology methods. Received: 2 August 1999 / Accepted: 25 October 1999     

Tensor constructions of open string theories (I) foundations

The possible tensor constructions of open string theories are analyzed from first principles. To this end the algebraic framework of open string field theory is clarified, including the role of the homotopy associative A_∞ algebra, the odd symplectic structure, cyclicity, star conjugation, and twist. It is also shown that two string theories are off-shell equivalent if the corresponding homotopy associative algebras are homotopy equivalent in a strict sense.It is demonstrated that a homotopy associative star algebra with a compatible even bilinear form can be attached to an open string theory. If this algebra does not have a space-time interpretation, positivity and the existence of a conserved ghost number require that its cohomology is at degree zero, and that it has the structure of a direct sum of full matrix algebras. The resulting string theory is shown to be physically equivalent to a string theory with a familiar open string gauge group.