Target Space Background Research Articles

Yang-Baxter deformations of the AdS5 \xd7 S5 pure spinor superstring

We present integrable Yang-Baxter deformations of the AdS5 × S5 pure spinor superstring theory which were obtained by using homological perturbation theory. Its equations of motion and BRST symmetry are discussed and its Lax connection is derived. We also show that its target space background is the same generalized supergravity background found for Yang-Baxter deformations of the Green-Schwarz superstring in AdS5 × S5.

Supergravity background of λ-deformed model for AdS2 × S2 supercoset

Starting with the Fˆ/G supercoset model corresponding to the AdSn×Sn superstring one can define the λ-model of arXiv:1409.1538 either as a deformation of the Fˆ/Fˆ gauged WZW model or as an integrable one-parameter generalisation of the non-abelian T-dual of the AdSn×Sn superstring sigma model with respect to the whole supergroup Fˆ. Here we consider the case of n=2 and find the explicit form of the 4d target space background for the λ-model for the PSU(1,1|2)/SO(1,1)×SO(2) supercoset. We show that this background represents a solution of type IIB 10d supergravity compactified on a 6-torus with only metric, dilaton Φ and the RR 5-form (represented by a 2-form F in 4d) being non-trivial. This implies that the λ-model is Weyl invariant at the quantum level and thus defines a consistent superstring sigma model. The supergravity solution we find is different from the one in arXiv:1410.1886 which should correspond to a version of the λ-model where only the bosonic subgroup of Fˆ is gauged. Still, the two solutions have equivalent scaling limit of arXiv:1504.07213 leading to the isometric background for the metric and eΦF which is related to the η-deformed AdS2×S2 sigma model of arXiv:1309.5850. Similar results are expected in the AdS3×S3 and AdS5×S5 cases.

Dynamical string tension in string theory with spacetime Weyl invariance

AbstractThe fundamental string length, which is an essential part of string theory, explicitly breaks scale invariance. However, in field theory we demonstrated recently that the gravitational constant, which is directly related to the string length, can be promoted to a dynamical field if the standard model coupled to gravity (SM+GR) is lifted to a locally scale (Weyl) invariant theory. The higher gauge symmetry reveals previously unknown field patches whose inclusion turn the classically conformally invariant SM+GR into a geodesically complete theory with new cosmological and possibly further physical consequences. In this paper this concept is extended to string theory by showing how it can be “Weyl lifted” with a local scale symmetry acting on target space background fields. In this process the string tension (fundamental string length) is promoted to a dynamical field, in agreement with the parallel developments in field theory. We then propose a string theory in a geodesically complete cosmological stringy background which suggests previously unimagined directions in the stringy exploration of the very early universe.

Pure spinor b-ghost in a super-Maxwell background

In the pure spinor formalism for the superstring, the b-ghost is a composite operator satisfying {Q,b}=T where Q is the pure spinor BRST operator and T is the holomorphic stress tensor. The b-ghost is holomorphic in a flat target-space background, but it is not holomorphic in a generic curved target-space background and instead satisfies $\bar\partial b$ = [Q, \Omega] for some \Omega. In this paper, \Omega\ is explicitly constructed for the case of an open superstring in a super-Maxwell background.

Canonical approach to Courant brackets for D-branes

We present an extension of the Courant bracket to the ones for Dp-branes by analyzing Hamiltonians and local superalgebras. Contrast to the basis of the bracket for a fundamental string which consists of the momentum and the winding modes, the ones for Dp-branes contain higher rank R-R coupling tensors. We show that the R-R gauge transformation rules are obtained by these Courant brackets for Dp-branes where the Dirac-Born-Infeld gauge field and the "two-vierbein field" play an essential role. Canonical analysis of the worldvolume theories naturally gives the basis of the brackets and the target space backgrounds keeping T-duality manifest at least for NS-NS sector. In a D3-brane analysis S-duality is manifest as a symmetry of interchanging the NS-NS coupling and the R-R coupling.

BORN'S RECIPROCAL GENERAL RELATIVITY THEORY AND COMPLEX NON-ABELIAN GRAVITY AS GAUGE THEORY OF THE QUAPLECTIC GROUP: A NOVEL PATH TO QUANTUM GRAVITY

Born's reciprocal relativity in flat space–times is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved space–times and construct a reciprocal general relativity theory (in curved space–times) as a local gauge theory of the quaplectic group and given by the semidirect product [Formula: see text], where the non-Abelian Weyl–Heisenberg group is H(1, 3). The gauge theory has the same structure as that of complex non-Abelian gravity. Actions are presented and it is argued why such actions based on Born's reciprocal relativity principle, involving a maximal speed limit and a maximal proper force, is a very promising avenue to quantize gravity that does not rely in breaking the Lorentz symmetry at the Planck scale, in contrast to other approaches based on deformations of the Poincaré algebra, quantum groups. It is discussed how one could embed the quaplectic gauge theory into one based on the U(1, 4), U(2, 3) groups where the observed cosmological constant emerges in a natural way. We conclude with a brief discussion of complex coordinates and Finsler spaces with symmetric and nonsymmetric metrics studied by Eisenhart as relevant closed-string target space backgrounds where Born's principle may be operating.

Non-Abelian coset string backgrounds from asymptotic and initial data

We describe hierarchies of exact string backgrounds obtained as non-Abelian cosets of orthogonal groups and having a space--time realization in terms of gauged WZW models. For each member in these hierarchies, the target-space backgrounds are generated by the ``boundary'' backgrounds of the next member. We explicitly demonstrate that this property holds to all orders in $\alpha'$. It is a consequence of the existence of an integrable marginal operator build on, generically, non-Abelian parafermion bilinears. These are dressed with the dilaton supported by the extra radial dimension, whose asymptotic value defines the boundary. Depending on the hierarchy, this boundary can be time-like or space-like with, in the latter case, potential cosmological applications.

R4, purified

We derive, using the pure-spinor formalism, the complete—including the fermions—4-point effective action of both type II superstrings to all orders in α′, at tree level in string loops. We find that, in the quartic-field approximation, the supergravity Lagrangian can be thought of as the tensor product, in a suitable sense, of two copies of the super-Yang–Mills Lagrangian in ten dimensions. The NS–NS 3-form enters the supergravity Lagrangian through a modified connection with torsion. As a byproduct, we derive the complete, i.e. to all orders in the θ-expansion, closed-string vertex operator in a flat target-space background.

OnQQ¯-potentials Derived via the AdS/CFT Duality

We give a short introduction to and a partial review of the work on the calculation of Wilson loops and QQ¯-potentials via the conjectured AdS/CFT duality. Included is a discussion of the relative weight of the stringy correction to the target space background versus the correction by the quantum fluctuations of the string world sheet.

Non-Abelian gauge field dynamics on matrix D-branes in curved space and two-dimensional σ-models

A survey is given of the formulation of a σ-model describing an open string moving in general target space background fields and coupling to both a matrix-valued D-brane position and a matrix-valued gauge field on the D-brane. The equations of motion for the D-brane and the gauge field are derived from the conformal invariance condition on the string world sheet in lowest order of α′. The ordering problem of the involved matrices is solved. In addition to our previous work we discuss a con ict between the classical T-duality rules and renormalization. The calculation of the RG β-functions does not yield the mass term obtained by formal application of these rules in the case of target space separated D-brane copies.

Q potential from AdS-CFT relation at T $\geq$ 0: Dependence on orientation in internal space and higher curvature corrections

Within the classical approximation we calculate the static $Q\bar Q$ potential via the AdS/CFT relation for nonzero temperature and arbitrary internal orientation of the quarks. We use a higher order curvature corrected target space background. For timelike Wilson loops there arises a critical line in the orientation-distance plane which is shifted to larger distances relative to the calculation with uncorrected background. Beyond that line there is no $Q\bar Q$-force. The overall vanishing of the force for antipodal orientation known from zero tempera ture remains valid. The spacelike Wilson loops yield a string tension for a (2+1)-dimensional gauge theory, independent of the relative internal orientation, but sensitive to the background correction.

Twisting the N=2 string.

The most general homogeneous monodromy conditions in $N{=}2$ string theory are classified in terms of the conjugacy classes of the global symmetry group $U(1,1)\otimes{\bf Z}_2$. For classes which generate a discrete subgroup $\G$, the corresponding target space backgrounds ${\bf C}^{1,1}/\G$ include half spaces, complex orbifolds and tori. We propose a generalization of the intercept formula to matrix-valued twists, but find massless physical states only for $\Gamma{=}{\bf 1}$ (untwisted) and $\Gamma{=}{\bf Z}_2$ (\`a la Mathur and Mukhi), as well as for $\Gamma$ being a parabolic element of $U(1,1)$. In particular, the sixteen ${\bf Z}_2$-twisted sectors of the $N{=}2$ string are investigated, and the corresponding ground states are identified via bosonization and BRST cohomology. We find enough room for an extended multiplet of `spacetime' supersymmetry, with the number of supersymmetries being dependent on global `spacetime' topology. However, world-sheet locality for the chiral vertex operators does not permit interactions among all massless `spacetime' fermions.

A new sigma model action for the four-dimensional Green-Schwarz heterotic superstring

The sigma model action described in this paper differs in four important features from the usual sigma model action for the four-dimensional Green-Schwarz superstring in a massless background. Firstly, the action is constructed on an N = (2, 0) super-worldsheet using a Kähler potential and a Ogievetsky-Sokatchev constraint; secondly, the target-space background fields are unconstrained; thirdly, the target-space dilaton couples to the two-dimensional curvative; and fourthly, the action reduces in a flat background to a free-field action. A conjecture is made for generalizing this N = (2, 0) sigma model action to the ten-dimensional Green-Schwarz heterotic superstring in a manner that preserves these four new features.

Deformations of superconformal field theories and target-space symmetries.

We give a method of deforming the conformal field theories of the bosonic and fermionic string corresponding to turning on the target-space background fields and describe a procedure for obtaining the transformations of the background fields under a target-space symmetry group. After illustrating these methods with examples, we apply them to the case of the chiral superfields which arise when the six internal dimensions of the fermionic string are compactified into a ${Z}_{3}$ orbifold and obtain the $N=1$ supersymmetry transformations of the chiral superfields.

World-sheet topology and target manifold in string theory.

We have examined the conformal anomaly cancellation in the nontrivial world-sheet topology of genus one to two-loop order in the target-space background expansion. The ..beta.. function for a given point in moduli space of torus turns out to be independent of the Teichmueller parameter giving the same equation of motion as obtained for the planar world sheet. In this computation, we have used a regularization scheme which is modular invariant.