Worldsheet Description of Exotic Five-brane with Two Gauged Isometries

We study the string worldsheet description of the background geometry of the exotic $5^2_2$-brane where two isometries are gauged. This is an extension of the gauged linear sigma model (GLSM) for the exotic $5^2_2$-brane with a single gauged isometry. The new GLSM with two gauged isometries has only ${\mathcal N}=(2,2)$ supersymmetry rather than ${\mathcal N}=(4,4)$ supersymmetry of the original GLSM. This is caused by a conflict between two different $SU(2)_R$ associated with the two gauge symmetries. However, if we take a certain limit, we can find the genuine string sigma model of the background geometry of the exotic $5^2_2$-brane with ${\mathcal N}=(4,4)$ supersymmetry. We also investigate the worldsheet instanton corrections to the background geometry of the exotic $5^2_2$-brane. The worldsheet instanton corrections to the string sigma model can be traced in terms of the two gauge fields in the new GLSM. This new GLSM gives rise to a different feature of the quantum corrections from the one in the GLSM with the single gauged isometry.Comment: 32 pages, accepted version in JHE

Semi-doubled Gauged Linear Sigma Model for Five-branes of Codimension Two

We establish a double dualization in two-dimensional supersymmetric gauge theory. We construct a gauged linear sigma model (GLSM) which contains a complex twisted linear superfield coupled to two sets of Abelian vector superfields. In the IR regime, the GLSM provides a string sigma model whose target spaces are a defect NS5-brane, a Kaluza-Klein vortex and an exotic $5^2_2$-brane. All of them are five-branes of codimension two and are related by T-duality. This model is a natural extension of the GLSM proposed by Tong which gives a sigma model for an H-monopole, i.e., a smeared NS5-brane of codimension three. This is also regarded as an alternative system of the GLSM for exotic five-branes proposed by the present authors. In this analysis, we confirm that the T-duality transformation procedure in terms of the complex twisted linear superfield is applicable to dualize both the real and imaginary parts of the twisted chiral superfield even at the UV level, beyond the IR limit. This indicates that the T-duality transformations at finite gauge couplings can be performed in terms of reducible superfields in the same way as irreducible (twisted) chiral superfields. Furthermore, we study quantum vortex corrections to the GLSM at the UV level. In the IR limit, these corrections are mapped to string worldsheet instanton corrections to the five-branes of codimension two. The result completely agrees with those in double field theory analysis.Comment: 46 pages, version published in JHE

World-volume Effective Action of Exotic Five-brane in M-theory

We study the world-volume effective action of an exotic five-brane, known as the M-theory 5${}^3$-brane (M5${}^3$-brane) in eleven dimensions. The supermultiplet of the world-volume theory is the $\mathcal{N} = (2, 0)$ tensor multiplet in six dimensions. The world-volume action contains three Killing vectors $\hat{k}_{\hat{I}} {}^M \ (\hat{I} =1,2,3)$ associated with the $U(1)^3$ isometry. We find the effective T-duality rule for the eleven-dimensional backgrounds that transforms the M5-brane effective action to that of the M5${}^3$-brane. We also show that our action provides the source term for the M5${}^3$-brane geometry in eleven-dimensional supergravityComment: 23 pages, comments and references added, version published in JHE

World-volume Effective Actions of Exotic Five-branes

We construct world-volume effective actions of exotic $5^2_2$-branes in type IIA and IIB string theories. The effective actions are given in fully space-time covariant forms with two Killing vectors associated with background isometries. The effective theories are governed by the six-dimensional $\mathcal{N}=(2,0)$ tensor multiplet and $\mathcal{N}=(1,1)$ vector multiplet, respectively. Performing the S-duality transformation to the $5^2_2$-brane effective action in type IIB string theory, we also work out the world-volume action of the $5^2_3$-brane. We discuss some additional issues relevant to the exotic five-branes in type I and heterotic string theories.Comment: 34 pages, 2 figures, typos corrected, figures replace

Worldsheet Instanton Corrections to Five-branes and Waves in Double Field Theory

We make a comprehensive study on the string winding corrections to supergravity solutions in double field theory (DFT). We find five-brane and wave solutions of diverse codimensions in which the winding coordinates are naturally included. We discuss a physical interpretation of the winding coordinate dependence. The analysis based on the geometric structures behind the solutions leads to an interpretation of the winding dependence as string worldsheet instanton corrections. We also give a brief discussion on the origins of these winding corrections in gauged linear sigma model. Our analysis reveals that for every supergravity solution, one has DFT solutions that include string winding corrections.Comment: 37 pages, version published in JHE