Gauge Five-brane Solutions of Co-dimension Two in Heterotic Supergravity

We continue to study the BPS gauge five-brane solutions of codimension two in ten-dimensional heterotic supergravity. The geometry including the dilaton and the NS-NS $B$-field are sourced from the monopole chain in $\mathbb{R}^2 \times S^1$. We find that the geometry is asymptotically Ricci flat and the dilaton is no longer imaginary valued. These properties are contrasted with the smeared counterpart discussed in our previous paper. We perform the T-duality transformations of the solution and find that it never results in a non-geometric object.Comment: 24 pages, 4 figures, typos corrected, version published in JHE

T-duality Transformation of Gauged Linear Sigma Model with F-term

We develop the duality transformation rules in two-dimensional theories in the superfield formalism. Even if the chiral superfield which we dualize involves an F-term, we can dualize it by virtue of the property of chiral superfields. We apply the duality transformation rule of the neutral chiral superfield to the ${\cal N}=(4,4)$ gauged linear sigma model for five-branes. We also investigate the duality transformation rule of the charged chiral superfield in the ${\cal N} = (4,4)$ gauged linear sigma model for the $A_1$-type ALE space. In both cases we obtain the dual Lagrangians in the superfield formalism. In the low energy limit we find that their duality transformations are interpreted as T-duality transformations consistent with the Buscher rule.Comment: 34 pages, version published in Nuclear Physics

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

Hyper-K\"ahler with Torsion, T-duality, and Defect (p,q) Five-branes

We investigate a five-branes interpretation of hyper-K\"{a}hler geometry with torsion (HKT). This geometry is obtained by conformal transformation of the Taub-NUT space which represents a Kaluza-Klein five-brane. This HKT would represent an NS5-brane on the Taub-NUT space. In order to explore the HKT further, we compactify one transverse direction, and study the $O(2,2;{\mathbb Z}) = SL(2,{\mathbb Z}) \times SL(2,{\mathbb Z})$ monodromy structure associated with two-torus. Performing the conjugate transformation, we obtain a new solution whose physical interpretation is a defect $(p,q)$ five-brane on the ALG space. Throughout this analysis, we understand that the HKT represents a coexistent state of two kinds of five-branes. This situation is different from composite states such as $(p,q)$ five-branes or $(p,q)$ seven-branes in type IIB theory. We also study the T-dualized system of the HKT. We again find a new solution which also indicates another defect $(p,q)$ five-brane on the ALG space.Comment: 21 pages, version published in JHE

Chiral Zeromodes on Vortex-type Intersecting Heterotic Five-branes

We solve the gaugino Dirac equation on a smeared intersecting five-brane solution in E_8\times E_8 heterotic string theory to search for localized chiral zeromodes on the intersection. The background is chosen to depend on the full two-dimensional overall transverse coordinates to the branes. Under some appropriate boundary conditions, we compute the complete spectrum of zeromodes to find that, among infinite towers of Fourier modes, there exist only three localized normalizable zeromodes, one of which has opposite chirality to the other two. This agrees with the result previously obtained in the domain-wall type solution, supporting the claim that there exists one net chiral zeromode localized on the heterotic five-brane system.Comment: 10 pages, 2 figure