Exactly solvable string compactifications on manifolds of SU(N) holonomy

A variety of heterotic string compactifications on the K3 surface, manifolds of SU(3) holomony, and higher holomony manifolds, are solved exactly. An example of the quintic hypersurface in CP₄ is worked out in detail. It is conjectured, and demonstrated in part, that any supersymmetric compactification of the heterotic string with an N=2 superconformal theory is equivalent to a compactification on a manifold of SU(N) holonomy, and in particular an arbitrary gluing of the discrete models with c=9 gives a solvable heterotic string compactification on some Calabi-Yau manifold. Calabi-Yau compactifications are seen to be exact vacua of string theory, retaining their topological and geometrical characteristics. Previously unknown enhanced gauge symmetries are found to arise for certain backgrounds.     

A heterotic N=2 string with space–time supersymmetry

We reconsider the issue of embedding space–time fermions into the four-dimensional N=2 worldsheet supersymmetric string. A new heterotic theory is constructed, taking the right-movers from the N=4 topological extension of the conventional N=2 string but a c=0 conformal field theory supporting target-space supersymmetry for the left-moving sector. The global bosonic symmetry of the full formalism proves to be U(1,1), just as in the usual N=2 string. Quantization reveals a spectrum of only two physical states, one boson and one fermion, which fall in a multiplet of (1,0) supersymmetry.     

No renormalization of the N=1 supergravity theory derived from the heterotic string

We show that one-loop string effects do not alter the form of the leading terms in the low-energy effective ten-dimensional N=1 supergravity theory derived from the heterotic string. We extend this result to the four-dimensional N=1 supergravity theory obtained after compactification, showing in particular that its Kähler potential is not renormalized by string loop effects or by the exchange of Kaluza-Klein modes. We also demonstrate that the Kähler potential and the gauge kinetic function are not renormalized by one-loop string effects in a wide class of four-dimensional formulations of superstring theories.     

Orbifold models and modular transformation

The orbifold models of the heterotic string are constructed on the quotient spaces of generalized tori by translational and rotational discrete symmetries. In order to obtain the consistent orbifold models, the conditions of the modular invariance are derived from a one-loop vacuum amplitude. Z₃ orbifold models satisfying such conditions are searched systematically. It is shown that there are infinite possible models with N = 2 supersymmetry. Among these models, two examples having E₆ and E₇ gauge groups are discussed. The orbifold models with N = 1 supersymmetry are also discussed in detail. It is shown that there are only five consistent models in the class of these models based on E₈ ⊗ E′₈ heterotic string in which the extra six-dimensional torus and the E₈ ⊗ E′₈ maximal torus are modded out by the rotational and the translational Z₃ symmetries respectively.     

Phenomenology and conformal field theory or can string theory predict the weak mixing angle?

We show that the weak mixing angle θ_w is the same for continuously connected classical vacua of the heterotic string which have chiral fermions in their massless spectra. We also show that the world-sheet quantum field theory for any classical vacuum with spacetime supersymmetry possesses an N = 2 superconformal invariance.     

New principles for string/membrane unification

The target space theory of the N = (2,1) heterotic string may be interpreted as a theory of gravity coupled to matter in either 1 + 1 or 2 + 1 dimensions. Among the target space theories in 1 + 1 dimensions are the bosonic, type II, and heterotic string world-sheet field theories in a physical gauge. The (2 + 1)-dimensional version describes a consistent quantum theory of supermembranes in 10 + 1 dimensions. The unifying framework for all of these vacua is a theory of (2 + 2)-dimensional self-dual geometries embedded in 10 + 2 dimensions. There are also indications that the N = (2,1) string describes the strong-coupling dynamics of compactifications of critical string theories to two dimensions, and may lead to insights about the fundamental degrees of freedom of the theory.     

Compactifications of F-theory on Calabi-Yau threefolds (II)

We continue our study of compactifications of F-theory on Calabi-Yau threefolds. We gain more insight into F-theory duals of heterotic strings and provide a recipe for building F-theory duals for arbitrary heterotic compactifications on elliptically fibered manifolds. As a byproduct we find that string/string duality in six dimensions gets mapped to fiber/base exchange in F-theory. We also construct a number of new N = 1, d = 6 examples of F-theory vacua and study transitions among them. We find that some of these transition points correspond upon further compactification to 4 dimensions to transitions through analogues of Argyres-Douglas points of N = 2 moduli. A key idea in these transitions is the notion of classifying (0,4) fivebranes of heterotic strings.     

Plane waves in effective field theories of superstrings

Exact plane wave solutions of d = 10, N = 1 Einstein-Yang-Mills supergravity theory are presented and their possible modifications in superstring effective theories are examined. It is found that the solutions are not affected by any of the known heterotic string corrections. It is argued that plane waves satisfy the effective field equations of the heterotic string theory in all powers of the string tension parameter α′, possibly after including a totally antisymmetric torsion field and reinterpreting the constants. Similar remarks also apply for type I superstrings. Further properties of the solutions are discussed.     

Heterotic string compactification on N = 2 superconformal theories with c = 9

We study (2, 2) compactifications of the heterotic string by tensoring the discrete N = 2 superconformal series. We construct all models with c = 9 that preserve N = 1 spacetime supersymmetry and discuss some of their properties.     

Non-perturbative superpotentials in string theory

The non-perturbative superpotential can be effectively calculated in M-theory compactification to three dimensions on a Calabi-Yau four-fold X. For certain X, the superpotential is identically zero, while for other X, a non-perturbative superpotential is generated. Using F-theory, these results carry over to certain Type IIB and heterotic string compactifications to four dimensions with N = 1 supersymmetry. In the heterotic string case, the non-perturbative superpotential can be interpreted as coming from space-time and world-sheet instantons; in many simple cases contributions come only from finitely many values of the instanton numbers.     

Non-perturbative gravitational corrections in a class of N = 2 string duals

We investigate the non-perturbative equivalence of some heterotic/type II dual pairs with N = 2 supersymmetry. The perturbative heterotic scalar manifolds are respectively SU(1, 1)/U(1) × SO(2,2+N_V)/SO(2) × SO(2+N_V) and SO(4,4+N_H)/SO(4) × SO(4+N_H) for moduli in the vector multiplets and hypermultiplets. The models under consideration correspond, on the type II side, to self-mirror Calabi-Yau threefolds with Hodge numbers h^1,1 = N_V + 3 = h^2,1 = N_H + 3, which are K3 fibrations. We consider three classes of dual pairs, with N_V = N_H = 8, 4 and 2. The models with h^1,1 = 7 and 5 provide new constructions, while the h^1,1 = 11, already studied in the literature, is reconsidered here. Perturbative R²-like corrections are computed on the heterotic side by using a universal operator whose amplitude has no singularities in the (T, U) space, and can therefore be compared with the type II side result. We point out several properties connecting K3 fibrations and spontaneous breaking of the N = 4 supersymmetry to N = 2. As a consequence of the reduced S- and T- duality symmetries, the instanton numbers in these three classes are restricted to integers, which are multiples of 2, 2 and 4, for N_V = 8, 4 and 2, respectively.     

New heterotic string theories in uncompactified dimensions < 10

It is shown that infinitely many heterotic string theories exist in uncompactified dimensions less than 10, that are one-loop finite (for massless external legs). Tachyons are removed by compactifying into tori (10 − d) and (26 −d) dimensions of the right-moving superstring and left-moving bosonic string sectors, respectively. The condition for modular invariance is shown to be equivalent to self-duality condition on even lorentzian lattices with (10 −d) and (26 −d) timelike and spacelike directions, respectively. The construction results in a (10 −d)(26 −d) parameter family of one-loop finite string theories. The zero mass sector of these theories for d = 4 and 6 correspond to N = 4 and 2 supergravity coupled to super Yang-Mills with many possible groups, some of which cannot be obtained by compactifying d = 10 heterotic string theory.     

Unification of gravity and elementary particle interactions in 26 dimensions?

The presence of an 11-cocycle in ten-dimensional theories containing an E₈×E₈ Yang-Mills theory coupled to supergravity suggests that the fundamental theory is a 26-dimensional string theory based on the Leech lattice. A theory with equal numbers of bosons and fermions is constructed by truncating a certain natural infinite-dimensional representation of the Monster sporadic group. This theory appears to be a certain combination of pieces of heterotic and N = 2 superstring.     

Orbifold compactifications with three families of Su(3) ×Su(2) ×U(1)n

We construct several N = 1 supersymmetric three-generation models with SU(3)×SU(2)×U(1)ⁿ gauge symmetry, obtained from orbifold compactification of the heterotic string in the presence of constant gauge-background fields. This Wilson-line mechanism also allows us to eliminate extra colour triplets which could mediate fast proton decay.     

Auxiliary supergravity fields,Chern-Simons terms and the heterotic string

The generating functional of target space S-matrix amplitudes is generalized to include auxiliary field and fermionic vertex operators. Using this formalism, a new Green-Schwarz mechanism associated with the auxiliary vector field of the four-dimensional, N=1 supergravity multiplet of the heterotic string is derived.     

Heterotic string theory: (II). The interacting heterotic string

The theory of interacting heterotic strings is presented. Vertex operators are derived in both the bosonic and fermionic formulations of the theory and are shown to be consistent with gauge invariance, Lorentz invariance, and supersymmetry. Three- and four-point amplitudes for the scattering of massless string states are calculated and used to derive the low-energy field theory limit of the heterotic string. Divergences in string theories are discussed and it is shown that one-loop heterotic string amplitudes are finite and modular invariant only for gauge group E₈×E₈ or spin (32)/Z₂.     

On the spectrum of (2,2) compactification of the heterotic string on conformal field theories

We study (2, 2) compactifications of the heterotic string by tensoring the degenerate N = 2 superconformal series. We recently constructed all models with c = 9 that preserve N = 1 spacetime supersymmetry. Here we extend this analysis by investigating the spectrum of our models. The number of generations and anti-generations is calculated and we comment on the conjectured relation between these conformal field theories and Calabi-Yau compactifications.     

N=2 superstrings in more than two dimensions?

For a string propagating in a Parisi-Sourlas superspace the critical dimension equals the difference in the number of positive-and negative-dimensional coordinates. In this way the dimension of the Minkowski subspace can be increased. Here we apply this to the N=2 superstring, with D_c=2 and find anomaly-free N=2 superstrings in all positive even dimensions. Nontrivial theories can be constructed from these N=2 theories by truncation: In a Parisi-Sourlas superspace with a ten-dimensional Minkowski subspace we find the N=1 NSR superstring, and with a four-dimensional Minkowski subspace we find an N=1 superstring, classically related to the D=10 NSR superstring by a canonical transformation.     

Superstring effects on D=4, N=1 supergravity

We give a lagrangian and supersymmetry transformation rules for the four-dimensional N=1 supergravity sector of superstring theories with their O(α′) corrections, obtained by the dimensional reduction á la Witten of the effective action of the ten-dimensional heterotic superstring. We also give general forms of O(α′ ″) corrections to supersymmetry transformation rules which arise through an axial vector superfield. Since our system is based on the ten-dimensional superstring without any auxiliary fields, our four-dimensional N=1 supergravity is free of auxiliary fields. Our point-field theory lagrangian is supposed to describe the mass-less fields in the untwisted sector of the ten-dimensional heterotic superstring propagating on orbifolds.