The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected. Conclusion unchange

Gaugino Condensation in Heterotic Fivebrane Background

The gaugino propagator is calculated by explicitly considering the propagation of a heterotic string between two different points in space-time using the non-trivial world-sheet conformal field theory for the fivebrane background. We find that there are no propagations of gaugino which is in the spinor representation of the non-trivial four-dimensional space of the fivebrane background. This result is consistent with the arguments on the fermion zero-modes of the fivebrane background in the low-energy heterotic supergravity theory. Furthermore, assuming the continuous limit to the flat space-time background at the place far away from the fivebrane, we suggest an effective propagator which is effective only at the place far away from the fivebrane in the flat space-time limit. From the effective propagator we evaluate a possible gaugino pair condensation. The result is consistent with the suggested scenario of the gaugino condensation in the fivebrane background in the low-energy heterotic supergravity theory.Comment: 14 page

Yang-Mills Equations of Motion for the Higgs Sector of SU(3)-Equivariant Quiver Gauge Theories

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory on spaces of the form R x SU(3)/H, with H equals either SU(2) x U(1) or U(1) x U(1). For the corresponding quiver gauge theory we derive the equations of motion and construct some specific solutions for the Higgs fields using different gauge groups. Specifically we choose the gauge groups U(6) and U(8) for the space R x CP^2 as well as the gauge group U(3) for the space R x SU(3)/U(1)xU(1), and derive Yang-Mills equations for the latter one using a spin connection endowed with a non-vanishing torsion. We find that a specific value for the torsion is necessary in order to obtain non-trivial solutions of Yang-Mills equations. Finally, we take the space R x CP^1 x CP^2 and derive the equations of motion for the Higgs sector for a U(3m+3) gauge theory.Comment: 21 pages, 4 figures; v2: figures added, references updated, published version (JMP

Dynamical supersymmetry analysis of conformal invariance for superstrings in type IIB R-R plane-wave

In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet conformal invariance for superstrings in type IIB R-R plane-wave in semi-light-cone gauge. Here we give further justification to the results found in that work through alternative arguments using dynamical supersymmetries. We show that by using the susy algebra the same quantum definition of the energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi identities we indirectly compute the Virasoro anomaly terms by calculating second order susy variation of the EM tensor. Certain integrated form of all such terms are shown to vanish. In order to deal with various divergences that appear in such computations we take a point-split definition of the same EM tensor. The final results are shown not to suffer from the ordering ambiguity as noticed in the previous work provided the coincidence limit is taken before sending the regularization parameter to zero at the end of the computation.Comment: 18 pages, Appendix B replaced by shorter argument in text (section 2.1), one reference adde

Quantization of Bosonic String Model in 26+2-dimensional Spacetime

We investigate the quantization of the bosonic string model which has a local U(1)_V * U(1)_A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations {\'a} la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in 26+2-dimensional background spacetime involving two time-like coordinates.Comment: 1+39 pages, no figures, LaTe

Gauge symmetries decrease the number of Dp-brane dimensions

It is known that the presence of antisymmetric background field $B_{\mu\nu}$ leads to noncommutativity of Dp-brane manifold. Addition of the linear dilaton field in the form $\Phi(x)=\Phi_0+a_\mu x^\mu$, causes the appearance of the commutative Dp-brane coordinate $x=a_\mu x^\mu$. In the present article we show that for some particular choices of the background fields, $a^2\equiv G^{\mu\nu}a_\mu a_\nu=0$ and $\tilde a^2\equiv [ (G-4BG^{-1}B)^{-1}\ ]^{\mu\nu}a_\mu a_\nu=0$, the local gauge symmetries appear in the theory. They turn some Neuman boundary conditions into the Dirichlet ones, and consequently decrease the number of the Dp-brane dimensions.Comment: We improve Sec.4. and Conclusion and we added the Appendix in order to clarify result

The surface states of topological insulators - Dirac fermion in curved two dimensional spaces

The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields the quantized charge Hall effect (\s_{xy}=(2n+1)e^2/h) will coexist with spin Hall effect.Comment: PRL accepted version, new information on thickness dependence adde

A Classical Manifestation of the Pauli Exclusion Principle

The occupied and unoccupied fermionic BPS quantum states of a type-IIA string stretched between a D6-brane and an orthogonal D2-brane are described in M-theory by two particular holomorphic curves embedded in a Kaluza-Klein monopole. The absence of multiply-occupied fermionic states --- the Pauli exclusion principle --- is manifested in M-theory by the absence of any other holomorphic curves satisfying the necessary boundary conditions. Stable, non-BPS states with multiple strings joining the D6-brane and D2-brane are described M-theoretically by non-holomorphic curves.Comment: harvmac 6 pages. Final version as published in JHE

Mass corrections in string theory and lattice field theory

Kaluza-Klein compactifications of higher dimensional Yang-Mills theories contain a number of four dimensional scalars corresponding to the internal components of the gauge field. While at tree-level the scalar zero modes are massless, it is well known that quantum corrections make them massive. We compute these radiative corrections at 1-loop in an effective field theory framework, using the background field method and proper Schwinger-time regularization. In order to clarify the proper treatment of the sum over KK--modes in the effective field theory approach, we consider the same problem in two different UV completions of Yang-Mills: string theory and lattice field theory. In both cases, when the compactification radius $R$ is much bigger than the scale of the UV completion ($R \gg \sqrt{\alpha'},a$), we recover a mass renormalization that is independent of the UV scale and agrees with the one derived in the effective field theory approach. These results support the idea that the value of the mass corrections is, in this regime, universal for any UV completion that respects locality and gauge invariance. The string analysis suggests that this property holds also at higher loops. The lattice analysis suggests that the mass of the adjoint scalars appearing in $\mathcal N=2,4$ Super Yang-Mills is highly suppressed due to an interplay between the higher-dimensional gauge invariance and the degeneracy of bosonic and fermionic degrees of freedom.Comment: 27 page