Nearby CFTs in the operator formalism: The role of a connection

The zero-momentum ghost-dilaton is a non-primary BRST physical state present in every bosonic closed string background. It is given by the action of the BRST operator on another state |χ , but remains nontrivial in the semirelative BRST cohomology. When local coordinates arise from metrics we show that dilaton and |χ insertions compute Riemannian curvature and geodesic curvature respectively. A proper definition of a CFT deformation induced by the dilaton requires surface integrals of the dilaton and line integrals of |χ . Surprisingly, the ghost number anomaly makes this a trivial deformation. While dilatons cannot deform conformal theories, they actually deform conformal string backgrounds, showing in a simple context that a string background is not necessarily the same as a CFT. We generalize the earlier proof of quantum background independence of string theory to show that a dilaton shift amounts to a shift of the string coupling in the field-dependent part of the quantum string action. Thus the "dilaton theorem", familiar for on-shell string amplitudes, holds off-shell as a consequence of an exact symmetry of the string action.

Section: The Cft Deformation Associated With the Dilatonmentioning

confidence: 99%

The dilaton theorem and closed string backgrounds

Bergman

Zwiebach

1995

“…In [7] marginal deformations were studied using a particular regularization method based on analytical continuation. There has been question both about the freedom to choose regularization and what it should look like [8,9,10]. Regularization by analytical continuation has also been considered in four dimensions, and has been shown to be equivalent to dimensional regularization [11].…”

Section: Introductionmentioning

confidence: 99%

Finite deformations of conformal field theories using analytically regularized connections

Gussich

Sundell

1997

We study some natural connections on spaces of conformal field theories using an analytical regularization method. The connections are based on marginal conformal field theory deformations.We show that the analytical regularization preserves conformal invariance and leads to integrability of the marginal deformations. The connections are shown to be flat and to generate well-defined finite parallel transport. These finite parallel transports yield formulations of the deformed theories in the state space of an undeformed theory. The restrictions of the connections to the tangent space are curved but free of torsion.

“…This is the connection Γ of Ref. [ 15], anticipated in Refs [ 13,14,20]. This connection, denoted hereafter as Γ, is best described (in the spirit of [ 16]) by indicating how to take covariant derivatives.…”

Section: Connections On Spaces Of Conformal Theoriesmentioning

confidence: 99%

“…[ 2,3] brought into the open an operator K which acting on a Riemann surface adds one special puncture throughout the surface minus the unit disks around the punctures (the disks that define the local coordinates around the punctures). This operation is intimately related, at the level of spaces of conformal theories, to the operation of covariant differentiation using a particular connection [ 13,14,15,16,17]. In addition to the operator K, a new family of moduli spaces of Riemann surfaces was introduced, spaces where the surfaces have one special puncture in addition to the ordinary punctures.…”

Section: Introductionmentioning

confidence: 99%

New moduli spaces from string background independence consistency conditions

Zwiebach

1996

In string field theory an infinitesimal background deformation is implemented as a canonical transformation whose hamiltonian function is defined by moduli spaces of punctured Riemann surfaces having one special puncture. We show that the consistency conditions associated to the commutator of two deformations are implemented by virtue of the existence of moduli spaces of punctured surfaces with two special punctures. The spaces are antisymmetric under the exchange of the special punctures, and satisfy recursion relations relating them to moduli spaces with one special puncture and to string vertices. We develop the theory of moduli spaces of surfaces with arbitrary number of special punctures and indicate their relevance to the construction of a string field theory that makes no reference to a conformal background. Our results also imply a partial antibracket cohomology theorem for the string action.