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.
We extend the classical heterotic instanton solutions to all orders in $α'$ using the equations of anomaly-free supergravity, and discuss the relation between these equations and the string theory $β$-functions.
We investigate the coset structures which appear in the dimensional reduction of supergravity theories. Especially we investigate how to recognize the global symmetry groups if the coset is non-split. As an example we apply our analysis to the theories emanating from the dimensional reduction of Heterotic supergravity.
We construct the heterotic dual theory in four dimensions of eleven dimensional supergravity compactified on a particular Joyce manifold, $J$. In particular, $J$ is constructed from resolving fixed point singularities of orbifolds of the seven torus in such a way that one is forced to consider a generalised orbifold on the heterotic side. We conjecture that a heterotic dual exists for all the compact 7-manifolds of $G_{2}$ holonomy constructed by Joyce.
Poly-vector deformations of heterotic supergravity solutions
Institute for Information Transmission Problems（信息传输问题研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）
We show that a choice of Pauli-Villars regulators allows the cancellation of all conformal and chiral anomalies in an effective field theory from Z_3 compactification of the heterotic string with two Wilson lines and an anomalous U(1).
This paper considers eleven dimensional supergravity on a manifold with boundary and the theories related to heterotic $M$-theory, in which the matter is confined to the boundary. New low energy actions and boundary conditions on supergravity fields are derived. Previous problems with infinite constants in the action are overcome. The new boundary conditions are shown to be consistent with supersymmetry, and their role in the ten dimensional reduction and gaugino condensation is briefly discussed.
Brane actions with chiral bosons present special challenges. Recent progress in the description of the two main examples -- the M theory five-brane and the heterotic string -- is described. Also, double dimensional reduction of the M theory five-brane on K3 is shown to give the heterotic string.
We explore the problem of braneworld black holes in the heterotic braneworld scenario of Lukas, Ovrut, Stelle and Waldram (LOSW). We show that black string solutions are unstable, and demonstrate some unusual asymptotics in the linearized metric. We also solve the fully coupled brane and bulk Einstein equations, finding an exact, though singular, solution which corresponds to a brane black hole in which the branes spike apart at the Schwarzschild radius.
We study non-perturbative effects due to a heterotic M-theory five-brane wrapped on Calabi-Yau threefold. We show that such instantons contribute to derivative F-terms described recently by Beasley and Witten rather than to the superpotential.
We consider the heterotic string on an elliptic Calabi-Yau three-fold with five-branes wrapping curves in the base ('horizontal' curves) of the Calabi-Yau as well as some elliptic fibers ('vertical' curves). We show that in this generalized set-up, where the association of the heterotic side with the $F$-theory side is changed relative to the purely vertical situation, the number of five-branes wrapping the elliptic fibers still matches the corresponding number of $F$-theory three-branes.
We construct vacua of heterotic M-theory with general gauge bundles and five-branes. Some aspects of the resulting low-energy effective theories are discussed.
We show how to construct the familiar heterotic NS5 brane as a topological soliton in a supercritical version of heterotic string theory. Closed string tachyon condensation removes the extra dimensions, leaving the NS5 in 10d, in a process highly reminiscent of the K-theoretical description of type II D-branes, but linking non-trivial gauge bundles and geometry. The construction requires a modification of the anomalous Bianchi identity for $H_3$ in supercritical heterotic string theory. We give various proofs for the existence of this modification.
We show that there exist two 27 and one 27bar of E6, net one chiral supermultiplet as zero modes localized on the intersecting 5-branes in the E8 x E8 heterotic string theory. A heterotic background is constructed by the standard embedding in the smeared solution, and the Dirac equation is solved explicitly on this background. It provides, after a compactification of some of the transverse dimensions, a Randall-Sundrum II like brane-world set-up in heterotic string theory.
The quantum consistency of sigma-models describing the dynamics of extended objects in a curved background requires the cancellation of their world-volume anomalies, which are conformal anomalies for the heterotic string and $SO(1,5)$ Lorentz-anomalies for the heterotic five-brane, and of their ten dimensional target space anomalies. In determining these anomalies in a $D=10$ Lorentz-covariant back-ground gauge we find that for the heterotic string the worldvolume anomalies cancel for 32 heterotic fermions while for the conjectured heterotic five-brane they cancel for only 16 heterotic fermion…
This paper constructs the reduction of heterotic $M$-theory in eleven dimensions to a supergravity model on a manifold with boundary in five dimensions using a Calabi-Yau three-fold. New results are presented for the boundary terms in the action and for the boundary conditions on the bulk fields. Some general features of dualisation on a manifold with boundary are used to explain the origin of some topological terms in the action. The effect of gaugino condensation on the fermion boundary conditions leads to a `twist' in the chirality of the gravitino which can provide an uplifting mechanism i…
Generalizing the work by Cherkis and Schwarz [1], we carry out the double dimensional reduction of supersymmetric M5 brane on K3 to obtain the supersymmetric action of heterotic string in 7-dimensional flat space-time. Motivated by this result, we propose the supersymmetric heterotic action in 10-dimensional flat space-time where the current algebra is realized in a novel way. We explicitly verify the kappa-symmetry of the proposed action.
We give a simple proof of the known S-duality of Heterotic String theory compactified on a T^6. Using this S-duality we calculate the tensions for a class of BPS 5-branes in Heterotic String theory on a circle. One of these, the Kaluza-Klein monopole, becomes tensionless when the radius of the circle is equal to the string length. We study the question of stability of the Heterotic NS5-brane with a transverse circle. For large radii the NS5-brane is absolutely stable. However for small radii it is only marginally stable. We also study the moduli space of 2 Kaluza-Klein monopoles and show that …
We obtain a family of heterotic supergravity backgrounds describing non-Kahler warped conifolds with three-form flux and an Abelian gauge bundle, preserving N=1 supersymmetry in four dimensions. At large distance from the singularity the usual Ricci-flat conifold is recovered. By performing a Z_2 orbifold of the T^{1,1} base, the conifold singularity can be blown-up to a four-cycle, leading to a completely smooth geometry. Remarkably, the throat regions of the solutions, which can be isolated from the asymptotic Ricci-flat geometry using a double-scaling limit, possess a worldsheet CFT descrip…
We explicitly construct massive (0,4) supersymmetric ADHM sigma models which have heterotic p-brane solitons as their conformal fixed points. These yield the familiar gauge 5-brane and a new 1-brane solution which preserve 1/2 and 1/4 of the spacetime supersymmetry respectively. We also discuss an analogous construction for the type II NS-NS p-branes using (4,4) supersymmetric models.
The open supermembrane contribution to the non-perturbative superpotential of bulk space five-branes in heterotic M-theory is presented. We explicitly compute the superpotential for the modulus associated with the separation of a bulk five-brane from an end-of-the-world three-brane. The gauge and kappa-invariant boundary strings of such open supermembranes are given and the role of the holomorphic vector bundle on the orbifold fixed plane boundary is discussed in detail.
We study F-theory duals of heterotic line bundle models on elliptically fibered Calabi-Yau threefolds. These models necessarily contain NS5-branes which are geometrised in the dual F-theory compactifications. We initiate a systematic study of the correspondence between various configurations of NS5-branes and the dual geometries in F-theory and perform several checks of the duality. Furthermore, we discuss the singular transitions between different configurations of NS5-branes.
We show that the gauge, gravitational (tangent-bundle) and their mixed anomalies arising from the localized modes near a 5-brane in the SO(32) heterotic string theory cancel with the anomaly inflow from the bulk with the use of the Green-Schwarz mechanism on the brane, similarly to the E_8 x E_8 5-brane case. We also compare our result with Mourad's analysis performed in the small-instanton limit.
Under heterotic/F-theory duality it was argued that a wide class of heterotic five-branes is mapped into the geometry of an F-theory compactification manifold. In four-dimensional compactifications this identifies a five-brane wrapped on a curve in the base of an elliptically fibered Calabi-Yau threefold with a specific F-theory Calabi-Yau fourfold containing the blow-up of the five-brane curve. We argue that this duality can be reformulated by first constructing a non-Calabi-Yau heterotic threefold by blowing up the curve of the five-brane into a divisor with five-brane flux. Employing hetero…
We derive the perturbative four-dimensional effective theory describing heterotic M-theory with branes and anti-branes in the bulk space. The back-reaction of both the branes and anti-branes is explicitly included. To first order in the heterotic strong-coupling expansion, we find that the forces on branes and anti-branes vanish and that the KKLT procedure of simply adding to the supersymmetric theory the probe approximation to the energy density of the anti-brane reproduces the correct potential. However, there are additional non-supersymmetric corrections to the gauge-kinetic functions and m…
We construct cosmological solutions of four-dimensional effective heterotic M-theory with a moving five-brane and evolving dilaton and T modulus. It is shown that the five-brane generates a transition between two asymptotic rolling-radii solutions. Moreover, the five-brane motion always drives the solutions towards strong coupling asymptotically. We present an explicit example of a negative-time branch solution which ends in a brane collision accompanied by a small-instanton transition. The five-dimensional origin of some of our solutions is also discussed.
The effective action for five-dimensional heterotic M-theory in the presence of five-branes is systematically derived from Horava-Witten theory coupled to an M5-brane world-volume theory. This leads to a five-dimensional N=1 gauged supergravity theory on S^1/Z_2 coupled to four-dimensional N=1 theories residing on the two orbifold fixed planes and an additional bulk three-brane. We analyse the properties of this action, particularly the four-dimensional effective theory associated with the domain-wall vacuum state. The moduli Kahler potential and the gauge-kinetic functions are determined alon…
We use Pauli-Villars regularization to evaluate the conformal and chiral anomalies in the effective field theories from Z3 and Z7 compactifications of the heterotic string without Wilson lines. We show that parameters for Pauli-Villars chiral multiplets can be chosen in such a way that the anomaly is universal in the sense that its coefficient depends only on a single holomorphic function of the three diagonal moduli. It is therefore possible to cancel the anomaly by a generalization of the four-dimensional Green-Schwarz mechanism. In particular we are able to reproduce the results of a string…
We study a system of $N_c$ $D3$-branes intersecting $D7$-branes and $O7$-planes in 1+1-dimensions. We use anomaly cancellation and string dualities to argue that there must be chiral fermion zero-modes on the $D3$-branes which are localized near the $O7$-planes. Away from the orientifold limit we verify this by using index theory as well as explicit construction of the zero-modes. This system is related to F-theory on K3 and heterotic matrix string theory, and the heterotic strings are related to Alice string defects in $\mathcal{N}=4$ Super-Yang-Mills. In the limit of large $N_c$ we find an $…
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 …
We find that the conjectured heterotic SO(32) five-brane sigma model develops necessarily k-anomalies, and we investigate their form. We show that these anomalies can be absorbed by modifications of the superspace constraints, that satisfy automatically the modified Bianchi-identity $dH_7=X_8$ of N=1, D=10 supergravity. The k-anomalies induce in particular a quantum deformation of the torsion constraint $T_{αβ}^a=2γ_{αβ}^a$.
We analyze the AdS_3 x M_7 type supersymmetric solutions, including non-trivial fluxes, of the Killing spinor equations in the heterotic supergravity. We classify these solutions by their G-structures and intrinsic torsions, for the cases that the number of seven-dimensional Killing spinors N are equal to 1,2,3 and 4. We find that the solutions cannot have non-trivial warp factor and the seven dimensional manifold M_7 is charactrized by G_2(SU(3))-structures for N=1 (2) case and SU(2)-structure for N=3 and 4 cases. They are further classified by their non-trivial intrinsic torsions. It is show…
Higher derivative couplings of hypermultiplets to $6D, N=(1,0)$ supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order $α'$ higher derivative corrections. Reduction on $T^4$ is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset $SO(4,4)/(SO(4)\times SO(4))$. While the $SO(4,4)$ symmetry is ensured by Sen's construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to r…
We construct the action for N M2-branes on $S^1/{Z}_2$. The resulting theory has a gauge anomaly but this can be cancelled if the two fixed point planes each support 8 chiral Fermions in the fundamental of U(N). Taking the low energy limit leads to the worldsheet theory of N free heterotic strings whose quantization induces an $E_8$ spacetime gauge symmetry on each fixed point plane. Thus this paper presents a non-abelian worldvolume analogue of the classic Horava-Witten analysis.
We present a Kahler potential for four dimensional heterotic M-theory which includes moduli describing a gauge five brane living on one of the orbifold fixed planes. This result can also be thought of as describing compactifications of either of the weakly coupled heterotic strings in the presence of a gauge five brane. This is the first example of a Kahler potential in these theories which includes moduli describing background gauge field configurations. Our results are valid when the solitons width is much smaller than the size scale of the Calabi-Yau threefold and can be used to provide a m…
We systematically consider heterotic SO(32) and E8 x E8 compactifications on K3 with Abelian and non-Abelian backgrounds as well as an arbitrary number of five-branes. The masses of the U(1) factors depend on the first Chern classes of the bundles and some combinatorial factors specifying the embedding in SO(32) or E8. The form of the generalised Green-Schwarz counter-terms in six dimensions constrains the possible heterotic five-brane actions. Some supersymmetric examples on K3 realisations as toric complete intersection spaces with up to three explicit two-forms are given.
We study T-duality chains of five-branes in heterotic supergravity where the first order $α'$-corrections are present. By performing the $α'$-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and the exotic $5^2_2$-brane solutions associated with the symmetric, the neutral and the gauge NS5-branes. We find that the Yang-Mills gauge field in these solutions satisfies the self-duality condition in the three- and two-dimensional transverse spaces to the brane world-volumes. The $O(2,2)$ monodromy structures of the $5^2_2$-brane solutions are investi…
We show that the same wrapping rules that have been derived for the branes of IIA and IIB string theory also apply to the branes of the toroidally compactified heterotic string theory. Moreover, we show that applying these wrapping rules to the IIA theory compactified over K3 is consistent with the well-known duality between the heterotic string theory compactified over T^4 and the IIA string theory compactified over K3. We derive a simple rule that relates, in any dimension, the T-duality representation of the branes of the toroidally compactified heterotic theory to the relevant R-symmetry r…
We study the dimensional reduction of the ${\cal N}=1$, ten-dimensional Heterotic Supergravity to four dimensions, at leading order in $α'$, when the internal space is a nearly-Kähler manifold. Nearly-Kähler manifolds in six dimensions are all the non-symmetric coset spaces and a group manifold. Here we reduce the theory using as internal manifolds the three six-dimensional non-symmetric coset spaces, omitting the case of the group manifold in the prospect of obtaining chiral fermions when the gauge fields will be included. We determine the effective actions for these cases, which turn out to …
We study heterotic/type I duality in d=8,9 uncompactified dimensions. We consider the special (``BPS saturated'') F^4 and R^4 terms in the effective one-loop heterotic action, which are expected to be non-perturbatively exact. Under the standard duality map these translate to tree-level, perturbative and non-perturbative contributions on the type I side. We check agreement with the one-loop open string calculation, and discuss the higher-order perturbative contributions, which arise because of the mild non-holomorphicities of the heterotic elliptic genus. We put the heterotic world-sheet insta…
In this note a simple calculation of one loop threshold corrections for the SO(32) heterotic string is performed. In particular the compactification on T^2 with a Wilson line breaking the gauge group to SO(16) x SO(16) is considered. Using heterotic type I duality, these corrections can be related to quantities appearing in the quantum mechanics of type I' D0 particles.
Generic heterotic M-theory compactifications contain five-branes wrapping non-isolated genus zero or higher genus curves in a Calabi-Yau threefold. Non-perturbative superpotentials do not depend on moduli of such five-branes.We show that fluxes and non-perturbative effects can stabilize them in a non-supersymmetric AdS vacuum. We also show that these five-branes can be stabilized in a dS vacuum, if we modify the supergravity potential energy by Fayet-Iliopoulos terms. This allows us to stabilize all heterotic M-theory moduli in a dS vacuum in the most general compactification scenarios. In add…
We show how, in heterotic M-theory, an M5-brane in the 11-dimensional bulk may end on an ``M9-brane'' boundary, the M5-brane boundary being a Yang monopole 4-brane. This possibility suggests various novel 5-brane configurations of heterotic M-theory, in particular a static M5-brane suspended between the two M9-brane boundaries, for which we find the asymptotic heterotic supergravity solution.
We study the warped geometry of heterotic M-Theory in five dimensions where five-branes are included in the bulk. Five-branes wrapping holomorphic curves lead to BPS configurations where the junction conditions are automatically satisfied. We consider five-branes wrapped around non-supersymmetric cycles and show that the configuration is unstable. We describe explicitly the resulting time-dependent geometry where the bulk five-branes move towards the Horova-Witten boundary walls. The five-branes collide with the boundary walls in a finite time resulting in the restoration of supersymmetry.
We construct a family of chiral anomaly-free supergravity theories in D=6 starting from D=7 supergravity with a gauged noncompact R-symmetry, employing a Horava-Witten bulk-plus-boundary construction. The gauged noncompact R-symmetry yields a positive (de Sitter sign) D=6 scalar field potential. Classical anomaly inflow which is needed to cancel boundary-field loop anomalies requires careful consideration of the gravitational, gauge, mixed and local supersymmetry anomalies. Coupling of boundary hypermultiplets requires care with the Sp(1) gauge connection required to obtain quaternionic Kahler…
On The Consistent Supersymmetric Reduction Of Heterotic Supergravity With Geometrically Arising Yang-Mills Symmetries
George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University（乔治·P和辛西娅·伍兹基础物理与天文学研究所，德克萨斯农工大学）；DAMTP, Centre for Mathematical Sciences, Cambridge University（剑桥大学数学科学中心DAMTP）
We consider the effective action of M-theory compactified on a S^1/Z_2 orbifold with R^2 interaction in the Gauss-Bonnet combination. We derive equations of motion with source terms arising from the Gauss-Bonnet terms and find the M2-brane solution up to order κ^{2/3}. It receives a correction which depends on the orbifold coordinate in the same form as the gauge 5-brane solution.
We present the potential energy due to flux and gaugino condensation in heterotic M-theory compactifications with anti-branes in the vacuum. For reasons which we explain in detail, the contributions to the potential due to flux are not modified from those in supersymmetric contexts. The discussion of gaugino condensation is, however, changed by the presence of anti-branes. We show how a careful microscopic analysis of the system allows us to use standard results in supersymmetric gauge theory in describing such effects - despite the explicit supersymmetry breaking which is present. Not surpris…
We present various (0,2) heterotic supercurrent supermultiplets in (1+1) dimensional quantum field theories. From the minimal supercurrent supermultiplets, we deduce conditions on symmetry enhancement such as Lorentz invariance, (chiral) dilatation invariance, R-invariance, (chiral) conformal invariance and their various combinations. Our construction covers many interesting and/or exotic possibilities such as Lifshitz supersymmetry and warped superconformal algebra. We also discuss the corresponding supergravity by gauging the supercurrent supermultiplet. In particular, we propose a novel cla…
We consider the 5-brane placed at one end of the world in the Heterotic $E_8 \times E_8$ theory. The low energy theory is a 6 dimensional $(1,0)$ superconformal theory with $E_8$ as a global symmetry. We calculate the two-point correlator of the $E_8$ current in 6 dimensions and in 4 dimensions after compactification on $\MT{2}$. This correlator is derived in 3 different ways: From field theory, from 11 dimensional supergravity and from F-theory.
We present the first example of a Kahler potential for heterotic M-theory which includes gauge bundle moduli. These moduli describe the background gauge field configurations living on the orbifold fixed planes. We concentrate on the bundle moduli describing the size and SU(2) orientation of a gauge five brane - a soliton which is primarily composed of these gauge fields. Our results are valid when the width of this object is small compared to the overall size of the Calabi-Yau threefold. We find that, in general, it is not consistent to truncate away these moduli in a simple manner.
