The covariant quantum superstring and superparticle from their classical actions (original) (raw)

Construction of the covariantly quantized heterotic superstring

Nuclear Physics B, 1990

We give a detailed discussion of the construction of the Batalin-Vilkovisky BRST charge for the heterotic superstring. In particular, we completely solve the higher-ghost sector using a recursion relation. The gauge choice W+ 0 = 0, which we previously proposed for the superparticle, leads to a free quantum action.

Improved covariant quantization of the heterotic superstring

Nuclear Physics B, 1991

A generalized lagrangian BRST formalism is developed and used to study the covariant quantization of the heterotic superstring. The quantum action is by construction invariant under the off-shell nilpotent BRST transformations, which is achieved by introducing a minimal set of auxiliary variables with nonzero ghost number. The method relies on the classical gauge structure, and represents a natural lagrangian extension of the ideas existing in the hamiltonian BRST approach.

Covariant Quantization of Superstrings Without Pure Spinor Constraints

Journal of High Energy Physics, 2002

We construct a covariant quantum superstring, extending Berkovits' approach by introducing new ghosts to relax the pure spinor constraints. The central charge of the underlying Kac-Moody algebra, which would lead to an anomaly in the BRST charge, is treated as a new generator with a new b − c system. We construct a nilpotent BRST current, an anomalous ghost current and an anomaly-free energy-momentum tensor. For open superstrings, we find the correct massless spectrum. In addition, we construct a Lorentz invariant B-field to be used for the computation of the integrated vertex operators and amplitudes.

Lorentz-covariant quantization of the heterotic superstring

Physics Letters B, 1989

We use the Batalin-Vilkovisky formalism to quantize the heterotic superstring in a gauge which manifestly preserves supersymmerry and Lorentz covariance. We explicitly construct the BV action before gauge-fixing in closed form, including the complicated four-ghost sector. The gauge-fixed action is completely quadratic and the conformal anomaly vanishes in d= 10.

Covariant superparticle quantization in a super Maxwell background

Physics Letters B, 1989

We extend our previous result on Lorentz-covariant quantization of a free superparticle in the gauge 0= 0 to the case of a super Maxwell background. In a general background, the action contains quintic and higher ghost couplings. We give the complete BRST charge before gauge fixing for the case of x-independent field strengths.

Existence, uniqueness and cohomology of the classical BRST charge with ghosts of ghosts

Communications in Mathematical Physics, 1989

A complete canonical formulation of the BRST theory of systems with redundant gauge symmetries is presented. These systems include p-form gauge fields, the superparticle, and the superstring. We first define the Koszul-Tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic. The global existence of the BRST generator is then demonstrated, and the BRST charge is proved to be unique up to canonical transformations in the extended phase space, which includes the ghosts. Finally, the BRST cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits, as in the irreducible case. This is done by re-expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree, which are identified with the ghosts of ghosts. The quantum cohomology is not dealt with.

Superparticle actions from superfields

Nuclear Physics B, 1994

Gauge invariant complex covariant actions for superparticles are derived from the field equations for the chiral superfields in a precise manner. The massive and massless cases in four dimensions are treated both free and in interaction with an external super Maxwell field. By means of a generalized BRST quantization these complex actions are related to real actions with second class constraints which are new in some cases.

The Canonical Structure of the Superstring Action

Canadian Journal of Physics, 2016

We consider the canonical structure of the Green–Schwarz superstring in 9 + 1 dimensions using the Dirac constraint formalism; it is shown that its structure is similar to that of the superparticle in 2 + 1 and 3 + 1 dimensions. A key feature of this structure is that the primary fermionic constraints can be divided into two groups using field-independent projection operators; if one of these groups is eliminated through use of a Dirac bracket then the second group of primary fermionic constraints becomes first class. (This is what also happens with the superparticle action.) These primary fermionic first-class constraints can be used to find the generator of a local fermionic gauge symmetry of the action. We also consider the superstring action in other dimensions of space–time to see if the fermionic gauge symmetry can be made simpler than it is in 2 + 1, 3 + 1, and 9 + 1 dimensions. With a 3 + 3 dimensional target space, we find that such a simplification occurs. We finally show ...