Perturbative String Theory Research Articles

Mirrorfolds with K3 fibrations

We study a class of non-geometric string vacua realized as completely soluble superconformal field theory (SCFT). These models are defined as `interpolating orbifolds' of K3 × S1 by the mirror transformation acting on the K3 fiber combined with the half-shift on the S1-base. They are variants of the T-folds, the interpolating orbifolds by T-duality transformations, and thus may be called `mirrorfolds'. Starting with arbitrary (compact or non-compact) Gepner models for the K3 fiber, we construct modular invariant partition functions of general mirrorfold models. In the case of compact K3 fiber the mirrorfolds only yield non-supersymmetric string vacua. They exhibit IR instability due to winding tachyon condensation which is similar to the Scherk-Schwarz type circle compactification. When the fiber SCFT is non-compact (say, the ALE space in the simplest case), on the other hand, both supersymmetric and non-supersymmetric vacua can be constructed. The non-compact non-supersymmetric mirrorfolds can get stabilised at the level of string perturbation theory. We also find that in the non-compact supersymmeric mirrorfolds D-branes are always non-BPS. These D-branes can get stabilized against both open- and closed-string marginal deformations.

Instantons, hypermultiplets and the heterotic string

Hypermultiplet couplings in type IIA string theory on a Calabi-Yau space can be quantum corrected by D2-brane instantons wrapping special Lagrangian cycles. On the other hand, hypermultiplet couplings in the heterotic string on a K3 surface are corrected by world-sheet instantons wrapping curves. In a class of examples, we relate these two sets of instanton corrections. We first present an analogue of the c-map for the heterotic string via a dual flux compactification of M-theory. Using this duality, we propose two ways of capturing quantum corrections to hypermultiplets. We then use the orientifold limit of certain F-theory compactifications to relate curves in K3 to special Lagrangians in dual type IIA compactifications. We conclude with some results from perturbative string theory for hypermultiplet F-terms and a conjecture about the topology of brane instantons.

Tree-level stability without spacetime fermions: novel examples in string theory

Is perturbative stability intimately tied with the existence of spacetime fermions in string theory in more than two dimensions? Type 0'B string theory in ten-dimensional flat space is a rare example of a non-tachyonic, non-supersymmetric string theory with a purely bosonic closed string spectrum. However, all known type 0' constructions exhibit massless NSNS tadpoles signaling the fact that we are not expanding around a true vacuum of the theory. In this note, we are searching for perturbatively stable examples of type 0' string theory without massless tadpoles in backgrounds with a spatially varying dilaton. We present two examples with this property in non-critical string theories that exhibit four- and six-dimensional Poincare invariance. We discuss the D-branes that can be embedded in this context and the type of gauge theories that can be constructed in this manner. We also comment on the embedding of these non-critical models in critical string theories and their holographic (Little String Theory) interpretation and propose a general conjecture for the role of asymptotic supersymmetry in perturbative string theory.

Minimal quiver standard model

This paper discusses the minimal quiver gauge theory embedding of the standard model that could arise from brane world type string theory constructions. It is based on the low energy effective field theory of D branes in the perturbative regime. The model differs from the standard model by the addition of one extra massive gauge boson, and contains only one additional parameter to the standard model: the mass of this new particle. The coupling of this new particle to the standard model is uniquely determined by input from the standard model and consistency conditions of perturbative string theory. We also study some aspects of the phenomenology of this model and bounds on its possible observation at the Large Hadron Collider.

Ultraviolet Properties of Maximal Supergravity

We argue that recent results in string perturbation theory indicate that the four-graviton amplitude of four-dimensional N=8 supergravity might be ultraviolet finite up to eight loops. We similarly argue that the h-loop M-graviton amplitude might be finite for h<7+M/2.

String Theory and M-Theory: A Modern Introduction

String theory is one of the most exciting and challenging areas of modern theoretical physics. This book guides the reader from the basics of string theory to recent developments. It introduces the basics of perturbative string theory, world-sheet supersymmetry, space-time supersymmetry, conformal field theory and the heterotic string, before describing modern developments, including D-branes, string dualities and M-theory. It then covers string geometry and flux compactifications, applications to cosmology and particle physics, black holes in string theory and M-theory, and the microscopic origin of black-hole entropy. It concludes with Matrix theory, the AdS/CFT duality and its generalizations. This book is ideal for graduate students and researchers in modern string theory, and will make an excellent textbook for a one-year course on string theory. It contains over 120 exercises with solutions, and over 200 homework problems with solutions available on a password protected website for lecturers at www.cambridge.org/9780521860697.

Local recoil of extended solitons: a string theory example

It is well-known that localized topological defects (solitons) experience recoil when they suffer an impact by incident particles. Higher-dimensional topological defects develop distinctive wave patterns propagating along their worldvolume under similar circumstances. For 1-dimensional topological defects (vortex lines), these wave patterns fail to decay in the asymptotic future: the propagating wave eventually displaces the vortex line a finite distance away from its original position (the distance is proportional to the transferred momentum). The quantum version of this phenomenon, which we call ``local recoil'', can be seen as a simple geometric manifestation of the absence of spontaneous symmetry breaking in 1+1 dimensions. Analogously to soliton recoil, local recoil of vortex lines is associated with infrared divergences in perturbative expansions. In perturbative string theory, such divergences appear in amplitudes for closed strings scattering off a static D1-brane. Through a Dirac-Born-Infeld analysis, it is possible to resum these divergences in a way that yields finite, momentum-conserving amplitudes.

Transcendentality and crossing

We discuss possible phase factors for theS-matrix of planar gauge theory, leading to modifications at four-loop order as compared to an earlierproposal. While these result in a four-loop breakdown of perturbative BMN scaling,Kotikov–Lipatov transcendentality in the universal scaling function for large-spintwist operators may be preserved. One particularly natural choice, unique up toone constant, modifies the overall contribution of all terms containing odd-zetafunctions in the earlier proposed scaling function based on a trivial phase. Excitingly,we present evidence that this choice is non-perturbatively related to a recentlyconjectured crossing-symmetric phase factor for perturbative string theory onAdS5 × S5 once the constant is fixed to a particular value. Our proposal, if true, might thereforeresolve the long-standing AdS/CFT discrepancies between gauge and string theory.

Corfu 05 lectures - part I: Strings on curved backgrounds

In these introductory lectures we summarize some basic facts and techniques about perturbative string theory (sections 1 to 6). These are further developed (sections 7 and 8) for describing string propagation in the presence of gravitational or gauge fields. We also remind some solutions of the string equations of motion, which correspond to remarkable (NS or D) brane configurations.A part II by Emilian Dudas will be devoted to orientifold constructions and applications to string model building.

Corfu 05 lectures - part II: Orientifolds and model building

These lectures contain an introduction in string theory with emphasize towards phenomenological applications. We present in particular the basis of orientifold constructions, the compactification from ten to four dimensions, intersecting brane world models, mechanisms for supersymmetry breaking, moduli stabilisation and the large extra dimensions models.Part I by Marios Petropoulos is devoted to basic techniques of perturbative string theory.

Causality, analyticity and an IR obstruction to UV completion

We argue that certain apparently consistent low-energy effective field theories described by local, Lorentz-invariant Lagrangians, secretly exhibit macroscopic non-locality and cannot be embedded in any UV theory whose S-matrix satisfies canonical analyticity constraints. The obstruction involves the signs of a set of leading irrelevant operators, which must be strictly positive to ensure UV analyticity. An IR manifestation of this restriction is that the "wrong" signs lead to superluminal fluctuations around non-trivial backgrounds, making it impossible to define local, causal evolution, and implying a surprising IR breakdown of the effective theory. Such effective theories can not arise in quantum field theories or weakly coupled string theories, whose S-matrices satisfy the usual analyticity properties. This conclusion applies to the DGP brane-world model modifying gravity in the IR, giving a simple explanation for the difficulty of embedding this model into controlled stringy backgrounds, and to models of electroweak symmetry breaking that predict negative anomalous quartic couplings for the W and Z. Conversely, any experimental support for the DGP model, or measured negative signs for anomalous quartic gauge boson couplings at future accelerators, would constitute direct evidence for the existence of superluminality and macroscopic non-locality unlike anything previously seen in physics, and almost incidentally falsify both local quantum field theory and perturbative string theory.

Cosmic superstrings stabilized by fermions

We show that there exist massive perturbative states of the ten-dimensional Green–Schwarz closed superstring that are stabilized against collapse due to presence of fermionic zero modes on its worldsheet. The excited fermionic degrees of freedom backreact on the spacetime motion of the string in the same way as a neutral persistent current would, rendering these string loops stable. We point out that the existence of these states could have important consequences as stable loops of cosmological size as well as long lived states within perturbative string theory.

String loop corrected hypermultiplet moduli spaces

Using constraints from supersymmetry and string perturbation theory, we determine the string loop corrections to the hypermultiplet moduli space of type II strings compactified on a generic Calabi-Yau threefold. The corresponding quaternion-Kahler manifolds are completely encoded in terms of a single function. The latter receives a one-loop correction and, using superspace techniques, we argue for the existence of a non-renormalization theorem excluding higher loop contributions.

The inside story: Quasilocal tachyons and black holes

We analyze the fate of excitations in regions of closed string tachyon condensate, a question crucial for understanding unitarity in a class of black holes in string theory. First we introduce a simple new example of quasilocal tachyon condensation in a globally stable AdS/CFT background, and review tachyons' appearance in black hole physics. Then we calculate forces on particles and fields in a tachyon phase using a field theoretic model with spatially localized exponentially growing time-dependent masses. This model reveals two features, both supporting unitary evolution in the bulk of spacetime. First, the growing energy of fields sourced by sets of (real and virtual) particles in the tachyon phase yields outward forces on them, leaving behind only combinations which do not source any fields. Secondly, requiring the consistency of perturbative string theory imposes cancellation of a BRST anomaly, which also yields a restricted set of states. Each of these effects supports the notion of a black hole final state arising from string-theoretic dynamics replacing the black hole singularity.

Two-loop string theory on null compactifications

We compute the two-loop contributions to the free energy in the null compactification of perturbative string theory at finite temperature. The cases of bosonic, type II and heterotic strings are all treated. The calculation exploits an explicit reductive parametrization of the moduli space of infinite-momentum frame string worldsheets in terms of branched cover instantons. Various arithmetic and physical properties of the instanton sums are described. Applications to symmetric product orbifold conformal field theories and to the matrix string theory conjecture are also briefly discussed.

M-theory and the string genus expansion

The partition function of the membrane is investigated. In particular, the case relevant to perturbative string theory of a membrane with topology S1×Σ is examined. The coupling between the string world sheet Euler character and the dilaton is shown to arise from a careful treatment of the membrane partition function measure. This demonstrates that the M-theory origin of the dilaton coupling to the string world sheet is quantum in nature.

Duality and higher derivative terms in M theory

Dualities of M-theory are used to determine the exact dependence on the coupling constant of the D6 4 interaction of the IIA and IIB superstring effective action. Upon lifting to eleven dimensions this determines the coefficient of the D6 4 interaction in eleven-dimensional M-theory. These results are obtained by considering the four-graviton two-loop scattering amplitude in eleven-dimensional supergravity compactified on a circle and on a two-torus — extending earlier results concerning lower-derivative interactions. The torus compactification leads to an interesting SL(2,)-invariant function of the complex structure of the torus (the IIB string coupling) that satisfies a Laplace equation with a source term on the fundamental domain of moduli space. The structure of this equation is in accord with general supersymmetry considerations and immediately determines tree-level and one-loop contributions to D64 in perturbative IIB string theory that agree with explicit string calculations, and two-loop and three-loop contributions that have yet to be obtained in string theory. The complete solution of the Laplace equation contains infinite series' of single D-instanton and double D-instanton contributions, in addition to the perturbative terms. General considerations of the higher loop diagrams of eleven-dimensional supergravity suggest extensions of these results to interactions of higher order in the low energy expansion.

Warped reheating in multi-throat brane inflation

We investigate in some quantitative details the viability of reheating in multi-throat brane inflationary scenarios by estimating and comparing the time scales for the various processes involved. We also calculate within perturbative string theory the decay rate of excited closed strings into KK modes and compare with that of their decay into gravitons; we find that in the inflationary throat the former is preferred. We also find that over a small but reasonable range of parameters of the background geometry, these KK modes will preferably tunnel to another throat (possibly containing the Standard Model) instead of decaying to gravitons due largely to their suppressed coupling to the bulk gravitons. Once tunneled, the same suppressed coupling to the gravitons again allows them to reheat the Standard Model efficiently. We also consider the effects of adding more throats to the system and find that for extra throats with small warping, reheating still seems viable.

String pair production in a time-dependent gravitational field

We study the pair creation of point particles and strings in a time-dependent, weak gravitational field. We find that, for massive string states, there are surprising and significant differences between the string and point-particle results. Central to our approach is the fact that a weakly curved spacetime can be represented by a coherent state of gravitons, and therefore we employ standard techniques in string perturbation theory. String and point-particle pairs are created through tree-level interactions between the background gravitons. In particular, we focus on the production of excited string states and perform explicit calculations of the production of a set of string states of arbitrary excitation level. The differences between the string and point-particle results may contain important lessons for the pair production of strings in the strong gravitational fields of interest in cosmology and black hole physics.

Collisions of cosmic F- and D-strings

Recent work suggests that fundamental and Dirichlet strings, and their (p,q) bound states, may be observed as cosmic strings. The evolution of cosmic string networks, and therefore their observational signals, depends on what happens when two strings collide. We study this in string perturbation theory for collisions between all possible pairs of strings; different cases involve sphere, disk, and annulus amplitudes. The result also depends on the details of compactification; the dependence on ratios of scales is only logarithmic, but this is still numerically important. We study a range of models and parameters, and find that in most cases these strings can be distinguished from cosmic strings that arise as gauge theory solitons.