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.     

On the associativity anomaly in open string field theory

The associativity anomaly in the star algebra of the open bosonic string is demonstrated by a simple oscillator calculation. In an associative algebra, formal arguments require that the “half string” BRST operator Q_L be nilpotent; however, we show that associativity is actually violated by computing Q_L² in an explicit operator representation of the star algebra.     

BRST operator on a Riemann surface

We discuss construction of the BRST operator for the bosonic closed string theory on an arbitrary Riemann surface of genus g>1. Using the BRST operator we prove the decoupling of the bosonic spurious physical states in general.     

Nilpotency ofQ BRST and background field equations

Following the method of Fradkin and Vialkovsky, we study the BRST charge operator.Q _BRST , for the closed bosonic string coupled to the background of its massless states. We show that the requirement of nilpotency ofQ _BRST gives rise to the correct equations for the background fields.     

From the first to the second quantized string theory

Starting from the hamiltonian formulation of the bosonic string we calculate the Feynman transition amplitude D. Inverting D we get the kinetic operator and thus the free field action.     

String quantization in accelerated frames and black holes

We quantize a closed bosonic string in a light-cone gauge in Rindler (uniformly accelerated) space-time and apply it to the Schwarzschild-Kruskal manifold. Inertial and accelerated particle states of the string associated to positive frequency modes with respect to the inertial and Rindler times respectively, are defined. There is a stretching effect of the string due to the presence of an event horizon. We explicitly solve the dynamical constraints leaving as physical degrees of freedom only those transverse to the acceleration. Different mass formulae are introduced depending on whether the centre of mass of the string has uniform speed or uniform acceleration. The expectation value of the Rindler (Schwarzschild) number-mode operator in the string around state (tachyon) results equal to a thermal spectrum at the Hawking-Unruh temperature T_s=α/2π (∼ M_Pl(M_Pl/M)^1/(D−3), where M is the black hole mass). We find T₀=M′/2π where M′ is the accelerated ground state string mass and T₀ the temperature T_s in dimensionless frequency units. Correlation functions of string coordinates and vertex operators and their Fourier transforms in accelerated time (string response functions) are computed and their thermal properties analyzed.     

N-string,g-loop vertex for the bosonic string

We construct the N-string, g-loop vertex V_N,g for the orbital degrees of freedom of the bosonic string in terms of the first abelian differentials, the period matrix and the prime form. We also build the |g> vacuum recently discussed by many people in the framework of an operator formalism on an arbitrary Riemann surface; our expression also contains the measure that takes into account the ghost contribution.     

BRS cohomology in string theory and the no-ghost theorem

It is shown that the operator counting the number of non-transverse modes of the bosonic string in 26 dimensions can be expressed as the anticommutator of the BRS charge Q with another operator. As a result it is easy to exhibit the cohomology of Q and express the transverse state projection operator of Brink and Olive in terms of Q.     

Conformal field theory and the symmetries of string field theory

The two-dimensional conformal field theory representation of Witten's bosonic string field theory is discussed. The basic overlap equations, K_n symmetry and BRST invariance are proved directly, without the usual expansion in oscillators. The conformal field theory approach naturally provides local overlap identities which (when integrated over half the string) can be used to verify properties of the cubic action. In particular, a recently proposed diffeomorphism invariance is shown to be free of anomalies. Finally, a new class of symmetries, including generalizations of the K_n symmetries which are local in spacetime, are presented.     

Covariant field theory of the compactified closed bosonic string

We covariantly first-quantize, via the BRST approach, the closed bosonic string compactified on a torus — in particular the 18-dimensional theory with E₈ × E₈ gauge bosons. Further, we give the corresponding free field theory. Thus the model is ready for the introduction of string interactions, and may be very useful for the study of gauge interactions in string theories.     

The calculation of planar one-loop diagrams in string theory using the BRS formalism

The fact is exploited that the operator counting the number of non-transverse modes for the bosonic string in 26 dimensions can be written as the anticommutator of the BRS charge Q with another operator to calculate planar one-loop diagrams. This results in a significant simplification over the earlier calculation of Brink and Olive.     

One loop partition functions in a compactified open bosonic string theory

We calculate the one loop partition functions of a toroidally compactified open bosonic string (fromD=26 toD=10) in the path integral formalism. By a certain combination of the compactified sectors it is shown that the partition functions of a compactified open bosonic string vanish in both annulus and Möbius strip topologies as in the open superstring case. We also discuss the consistency requirement for the equivalence between the compactified open bosonic string and the open superstring with the gauge groups (SO(8192) andSO(32), respectively.     

BRST invariant tadpole operator in the bosonic string

Using a BRST invariant three-reggeon vertex we construct an explicit expression for the BRST invariant planar tadpole operator for the bosonic string. Joined to an (N+1)-reggeon vertex it yields the correct expression for the one-loop N-tachyon amplitude.     

The heterotic string and supersymmetric counterparts of the Lorentz Chern-Simons terms

The heterotic string three-point amplitude, which involves two fermionic and one bosonic state, determines some of the terms that must be added to the action of the N=1 supergravity coupled to N=1 supersymmetric Yang-Mills in ten dimensions to preserve supersymmetry, if the Lorentz Chern-Simons term is included in the definition of the field strength H_μνϱ for the cancellation of anomalies. Our calculation reveals an interesting structure, which suggests that the relevant H-Bianchi for the analysis of possible heterotic string compactifications involves a spin connection possibly with torsion.     

Field quantization in non-archimedean field theory

A formulation of field quantization of bosonic and fermionic fields defined on the disconnected field of p-acid numbers Q _p is given. We introduce a canonical quantization procedure and exhibit the properties of the nonlocal operators present in the action. Its relevance to string theory on Q _p is also discussed.     

A path-dependent supersymmetric field theory of electric and magnetic charges

We present a supersymmetric field theory of electric and magnetic charges with a genuine string. As a consequence of the conventional and representation preserving constraints, the superstring variable has only a bosonic (space-time) part ξ^μ. We discuss the string-independence of the theory.     

BRST quantization in the Siegel gauge

From a formal generalization to N copies of the free open string field theory BRST-quantized in the Siegel gauge we reproduce the BRST quantization of the free closed bosonic string field theory and obtain the one of massless higher spin field theories.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

The multiloop covariant tadpole operator and amplitudes for the bosonic string

An explicit expression is given for the covariant tadpole operator with an arbitrary number of loops, including the ghost zero mode contribution. Its integrand is recast in geometrical terms and is recognized to give the g-vacuum for the bosonic string recently discussed in the literature. By joining the g-tadpole to an N-reggeon vertex the general orientable dual amplitude with g loops is obtained.     

Pseudo-supergravity extension of the bosonic string

We construct a “pseudo-supersymmetric” fermionic extension of the effective action of the bosonic string in arbitrary spacetime dimension D. The theory is invariant under pseudo-supersymmetry transformations up to the quadratic fermion order, which is sufficient in order to be able to derive Killing spinor equations in bosonic backgrounds, and hence to define BPS type solutions determined by a system of first-order equations. The pseudo-supersymmetric theory can be extended by coupling it to a Yang-Mills pseudo-supermultiplet. This also allows us to construct “α^′ corrections” involving quadratic curvature terms. An exponential dilaton potential term, associated with the conformal anomaly for a bosonic string outside its critical dimension, can also be pseudo-supersymmetrised.