Narrow Results

We present a path integral formalism to review the effective dynamics of an arbitrary and curved Dirichlet p-brane (Dp-brane) in open bosonic string and subsequently in type I superstring theory. We obtain the perturbative corrections to the Dirac–Born–Infeld dynamics up to in the presence of an antisymmetric two-form B field. A part of the corrections can be seen to be associated with an ultraviolet divergence. Renormalization of the Dp-brane collective coordinates is performed to show that the residual corrections lead to a noncommutative description on the world volume. The Dp-brane modes are analyzed and we show that its zero modes play a vital role in noncommutative geometry. Our analysis facilitates the noncommutative world volume description for an arbitrary B field.

In this paper we study the phenomenon of UV/IR mixing in noncommutative field theories from the point of view of worldsheet open–closed duality in string theory. New infrared divergences in noncommutative field theories arise as a result of integrating over high momentum modes in the loops. These are believed to come from integrating out additional bulk closed string modes. We analyze this issue in detail for the bosonic theory and further for the supersymmetric theory on the C²/Z₂ orbifold. We elucidate on the exact role played by the constant background B-field in this correspondence.

We explicitly solve the classical equations of motion for strings in backgrounds obtained as non-Abelian T-duals of a homogeneous isotropic plane-parallel wave. To construct the dual backgrounds, semi-Abelian Drinfeld doubles are used which contain the isometry group of the homogeneous plane wave metric. The dual solutions are then found by the Poisson–Lie transformation of the explicit solution of the original homogeneous plane wave background. Investigating their Killing vectors, we have found that the dual backgrounds can be transformed to the form of more general plane-parallel waves.

We investigate the dependence of non-Abelian T-duality on various identification of the isometry group of target space with its orbits, i.e. with respect to the location of the group unit on manifolds invariant under the isometry group. We show that T-duals constructed by isometry groups of dimension less than the dimension of the (pseudo)-Riemannian manifold may depend not only on the initial metric but also on the choice of manifolds defining positions of group units on each of the submanifold invariant under the isometry group. We investigate whether this dependence can be compensated by coordinate transformation.

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of 11-dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and $SL(5)$ U-duality groups reduce to the $SO(2,2)$ and $SO(3,3)$ T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group $E_d(Z)$.

The higher-derivative ${\alpha }^{\prime }$ corrections consistent with $O(d,d)$ duality invariance can be completely classified for cosmological, purely time-dependent backgrounds. This result is used to show that there are duality invariant theories featuring string-frame de Sitter vacua as solutions that are nonperturbative in ${\alpha }^{\prime }$, thus suggesting that classical string theory may realize de Sitter solutions in an unexpected fashion.

The AGT-W relation is a conjecture of the nontrivial duality between 4-dim quiver gauge theory and 2-dim conformal field theory. We verify a part of this conjecture for all the cases of quiver gauge groups by studying on the property of 3-point correlation function of conformal theory. We also mention the relation to algebra as one of the promising direction towards the proof of the remaining part.

Double field theory promotes the T-duality of closed string theory to a manifest symmetry, thus leading to a new perspective on the geometry experienced by stringy probes. In this contribution, we discuss the mathematical structure underlying the symmetries of double field theory, thus defining a DFT algebroid. We trace its origins in a large Courant algebroid defined over a doubled geometry, and show that after imposing a section condition the DFT algebroid reduces to a canonical Courant algebroid, as expected in generalized geometry.