Ghost Fields Research Articles

DISC AND RP2 CORRECTIONS TO THE STRING EFFECTIVE LAGRANGIAN

Bosonic string scattering amplitudes on the disc and the projective plane are compared with amplitudes from the effective field theory derived by demanding consistency of string propagation in background massless fields. Path integral (as opposed to BRST) quantization is used throughout, with the ghost fields integrated out. We point out a difficulty in defining a covariant dilaton vertex operator in this formalism. A nonstandard graviton vertex operator is constructed, by which we compute the vacuum energy for the two topologies and find that it has the correct ratio to the dilaton tadpole, as predicted by the effective Lagrangian. Factorization of tadpole divergences in N-point amplitudes leads to the same result, modulo a paradox discovered by Fischler, Klebanov, and Susskind, which is reviewed. We also show that the dilaton two- and three-point functions agree with the exponential form of the dilaton potential in the effective action, despite quadratic divergences that initially appear in these amplitudes.

Hidden BRS invariance in classical mechanics. II.

In this paper we develop a path-integral formulation of {ital classical} Hamiltonian dynamics, that means we give a functional-integral representation of {ital classical} transition probabilities. This is done by giving weight one'' to the classical paths and weight zero'' to all the others. With the help of anticommuting ghosts this measure can be rewritten as the exponential of a certain action {ital {tilde S}}. Associated with this path integral there is an operatorial formalism that turns out to be an extension of the well-known operatorial approach of Liouville, Koopman, and von Neumann. The new formalism describes the evolution of scalar probability densities and of {ital p}-form densities on phase space in a unified framework. In this work we provide an interpretation for the ghost fields as being the well-known Jacobi fields of classical mechanics. With this interpretation the Hamiltonian {ital {tilde H}}, derived from the action {ital {tilde S}}, turns out to be the Lie derivative associated with the Hamiltonian flow. We also find that the action {ital {tilde S}} presents a set of Becchi-Rouet-Stora- (BRS-)type invariances mixing the original phase-space variables with the ghosts. Together with a Sp(2) symmetry of the pure ghosts sector, they form a {ital universal}more » invariance group ISp(2) which is present in any Hamiltonian system. The physical and geometrical meaning of the ISp(2) generators is discussed in detail: in particular the conservation of one of the generators is shown to be equivalent to the Liouville theorem. The ISp(2) algebra is then used to give a modern operatorial reformulation of the old Cartan calculus on symplectic manifolds.« less

Strings on world-sheet orbifolds

A new orbifold construction is proposed in which orbifold groups can also act on the ghost fields. The crucial role of BRST invariance in the construction is analyzed. Type-I superstrings (on ordinary orbifolds) fit naturally into this scheme as world-sheet orbifolds of the type-II superstring theory. More exotic examples are presented as well. Finally, some geometrical aspects of the construction are discussed.

The ghost structure of the superstring

The infinite towers of ghost fields that arise in the space-time supersymmetric formulation of the superstring fit into vector and metaplectic (spinor) representations of OSp( p, q|2 m) supergroups. Conventional and “twisted” metaplectic representations of these groups are presented and the conditions on p, q and m that allow the OSp analogues of Majorana and Majorana-Weyl constraints are found. Invariant inner products of these representations are constructed and possible connections with the quantum action of the superstring are discussed.

Weil algebra structure and geometrical meaning of BRST transformation in topological quantum field theory

The Weil algebra structure of the BRST transformation of topological quantum field theory is investigated. This structure appears in the gauge and ghost fields sector and is common to both topological quantum field theory and BRS gauge fixed non-abelian gauge theory. By the Weil algebra structure, we can derive the descent equations of topological quantum field theory which generate the Donaldson polynomials. The algebraic structure also reveals the geometrical meaning of the ghost fields ψ and ϕ in topological quantum field theory as the components of the total curvature.

Consequence of local U(1)V x U(1)A symmetry in two dimensions.

We study the two-dimensional U(1){sub {ital V}}{times}U(1){sub {ital A}} model in detail. This model has both local vector U(1) and local axial-vector U(1) gauge symmetries. The original Lagrangian is expressed in terms of some fermion fields and a gauge field. We bosonize fermion fields by the same method as in the Thirring model. The U(1){sub {ital V}}{times}U(1){sub {ital A}} symmetry requires the vanishing of the Schwinger term (or, equivalently, the nilpotency of the Becchi-Rouet-Stora-Tyutin charge). The absence of the Schwinger term leads to some negative-norm states (ghost fields). However, the physical states are positive semidefinite if and only if the number of ghost fields is only one. We show the no-ghost theorem in detail.

Auxiliary ghost fields in statistical dynamics

The path integral formulation of statistical dynamics involves a functional determinant whose role within the theory has remained somewhat unclear. This has occasionally led to incorrect generalizations of the formalism to the case of multiplicative random forces. We present a hidden symmetry of the theory and show how it can be used to clarify these issues. Important further applications are also pointed out.

Problem of changing gauge in Polyakov's theory: Relation between light-cone and conformal gauges.

The problem of the change of gauge in string theory is discussed in the context of the functional-integral formulation of the theory. The equivalence between the light-cone and conformal gauges is shown. By performing a proper change of variables in commuting and ghost fields in the functional integral of Polykov's theory, the string theory in the conformal gauge is obtained from the light-cone gauge-fixed theory. Finally, the problem of changing gauge has been generalized to the higher-genus surfaces. It has been shown that string theory in the conformal gauge is equivalent to the light-cone gauge-fixed theory of strings, for surfaces with an arbitrary number of handles.

Covariant superstring fermionic amplitudes, vertex operators and picture changing

Massive Ramond and Neveu-Schwarz vertex operators in the − 1 2 and −1 ghost representations respectively are obtained from the factorization of the scattering amplitude of an arbitrary number of bosonic and fermionic massless states on general Riemann surfaces. The correlators for the ghost field of charge -1 and its derivatives are given as well as the normal ordering prescriptions to be used in computing scattering amplitudes. The vertex operators for the massless and the first two excited levels, both of the Ramond and the Neveu-Schwarz sector are given explicitly. The picture changing mechanism is considered and applied to relate the Neveu-Schwarz vertices in different representations.

Feynman-like rules for bosonic strings; Tree vertices, b-ghost insertion and factorization

Feynman-like rules for constructing string vertices are formulated in the operator formalism in such a way that the underlyinh geometrical picture becomes manifest. Using Olive's as well as Lovelace's parametrization for the matter part we complete Feynman-like rules by including the ghost fields. The twisted propagator is defined with a b-ghost insertion together with a contour integration, in order to take the measure properly into account. The measure part of the string vertex is analyzed in detail. We formulate the BRST-invariant N-string tree vertex which enjoys the exact factorization property.

A UNIFIED APPROACH TO THE COMPUTATION OF CENTRAL TERMS IN KAC-MOODY AND VIRASORO ALGEBRAS

A theorem is established which gives a unified formula for the commutator of two bilinear Kac-Moody (KM) or Virasoro (V) currents in terms of these currents and a central term. The formula not only covers the standard bilinear cases previously considered (V currents of matter, string, ghost and KM fields, and KM currents of free fields) but also the two twisted cases, namely the V currents of twisted KM fields and twisted KM currents of free fields. It is also shown that in BRST theory the central term C is always the Hessian of the BRST charge Q2 (which explains the well-known equivalence of C = 0 and Q2 = 0).

GAUGE-INVARIANT RENORMALIZABILITY OF NON-ABELIAN STOCHASTICALLY QUANTIZED THEORIES

The generating functional of a stochastically quantized non-Abelian theory is formulated in a gauge-invariant form in the nonequilibrium phase in (D + 1) dimensions. In the gauge [Formula: see text], μ = 1, … D, in the case of dimensional regularization, this formulation is shown to be completely equivalent (in perturbation theory) to the usual stochastic quantization with an addition to the Langevin equation of the Zwanziger type term [Formula: see text] for a rather wide class of functionals υ (A). In dimensional regularization, the determinant due to ghost fields is equal to unity in perturbation theory but has Gribov's zeros in nonperturbative calculations. The effective action in a generating functional possesses BRST-symmetry from which one can derive Ward-Fradkin-Takahashi-Slavnov-Taylor identities (WI) that provide the connections between the renormalization constants of vertices and fields and the gauge-invariant renormalizability of the theory in nonequilibrium and equilibrium phases for D ≤ 4. The renormalization constants of fields and parameters are calculated in dimensional regularization in the one-loop approximation; it is shown that due to the nontrivial renormalization of the kinetic coefficient in nonequilibrium phase, the β functions turn out to be distinct in these phases, in four dimensions the β function coinciding with the ordinary one in equilibrium phase. Fulfillment of the principal WI in perturbation theory is checked.

COSET SPACE DIMENSIONAL REDUCTION AND GAUGE FIXING OVER THE SUPERCIRCLE

The constraints of CSDR are solved for vector gauge fields over a coset space IOSp (1/2, R)/ OSp (1/2, R) including supertranslations (extended BRST transformations) and ordinary translations (rotations on the circle). The gauge-fixing action incorporates standard ghost and multiplier fields (and their modes) but is nonpolynomial in an additional scalar field ϕ and its modes. There is a new "ϕ-BRST" invariance with respect to ϕ dependent gauge transformations, a bosonic counterpart of the usual "ghost-BRST" invariance. In the Abelian case, ϕ can be integrated out, leading to a formalism equivalent to ordinary covariant gauge-fixing.

Vanishing of the chiral anomaly for an antisymmetric tensor field

We consider a gauge antisymmetric tensor field (which is equivalent to a massless scalar field on-mass-shell). We demonstrate that the total chiral current which accounts for the chirality of the vector ghost fields is not anomalous. We also dwell on the relation between the number of zero modes of the antisymmetric tensor field and the anomaly in the chiral current of the vector field.

Wilson-loop symmetry breaking reexamined

The splitting in energy of gauge field vacua on the non-simply connected space S 3/Z 2 is reconsidered. We show the calculation to the one-loop level for a Yang-Mills vector with a ghost field. We confirm our previous result and give a solution to the question posed by Freire, Romão and Barroso.

Geometro-stochastic quantization of gauge fields in curved space-time

It is shown that the geometro-stochastic method of quantization of massive fields in curved space-time can be extended to the massless cases of electromagnetic fields and general Yang-Mills fields. The Fock fibres of the massive case are replaced in the present context by fibres with indefinite inner products, such as Gupta-Bleuler fibres in the electromagnetic case. The quantum space-time form factor used in the massive case gives rise in the present case to quantum gauge frames whose elements are generalized coherent states corresponding to pseudounitary spin-one representations of direct products of the Poincare group with theU(1),SU(N) or other internal gauge groups. Quantum connections are introduced on bundles of second-quantized frames, and the corresponding parallel transport is expressed in terms of path integrals for quantum frame propagators. In the Yang-Mills case, these path integrals make use of Faddeev-Popov quantum frames. It is shown, however, that in the present framework the ghost fields that give rise to these frames possess a geometric interpretation related to the presence of a super-gauge group that, in addition to the external Poincare and Yang-Mills gauge degrees of freedom, involves also the internal ones related to choices of gauge bases within the quantum fibres.

VERTEX OPERATOR REPRESENTATION OF OSp(M|N)(1)

Using the boson-fermion equivalence in 2-d conformal field theory and the boson-boson equivalence of the superconformal bosonic ghost fields of the string theory, we construct a level k=+1 representation of the affine superalgebra OSp (M|N)(1) in terms of vertex operators.

Covariant off-shell string amplitudes with auxiliary fields

We employ BRST invariance to explicitly determine the ghost part of the four-point vertex in Witten's open, bosonic, string field theory. This allows the computation of any covariant off-shell four-point amplitude involving physical as well as first-quantized auxiliary or second-quantized Faddeev-Popov ghost fields. We display some examples and complete the proof of associativity of the star product.

THE COVARIANT CONSISTENT QUANTIZATION OF BOSONIZED CHIRAL SCHWINGER MODEL

From Ward-Takahashi identities and full propagators, we obtain a massive Proca field Uμ which has the positive norm state. There also exists a massless physical scalar field H which turns out to be the positive norm state only for 4e2>1. It is further shown that a dipole ghost field D and auxiliary field B, as quartet members, belong to the zero norm states.

Sewing closed string amplitudes

We give a prescription for combining the Polyakov amplitudes for two string world-sheets with boundary by functionally integrating over boundary values of the embedding and ghost fields. The relationship between the moduli of the sewn surface and its components is investigated, and implications for string field theory are discussed.