What Makes a Theory Testable, or Is Intelligent Design Less Scientific Than String Theory?

I compare the theory of intelligent design to string theory to see on what basis, if any, only the former can be justifiably excluded as being scientific.We shall see that the classic criterion of testability or falsifiability is sometimes not so straightforward, and that there are other criteria to help us make such a distinction.     

String creation in cosmologies with a varying dilaton

FRW solutions of the string theory low-energy effective actions are described, yielding a dilaton which first decreases and then increases. We study string creation in these backgrounds and find an exponential divergence due to an initial space-like singularity. We conjecture that this singularity may be removed by the effects of back-reaction, leading to a solution which at early times is de Sitter space.     

Instanton and eigenmodes in a two-dimensional theory of gravity with torsion

Instanton-like solutions characterizing the geometric structure of the manifold are found to be in a two-dimensional theory of gravity with dynamical metric and torsion in the context of string theory. The eigenmodes for fluctuations of the solutions of the equations are also investigated and it has been shown that these solutions are stable.     

On the universality of string theory

String theory is accused by some of its critics to be a purely abstract mathematical discipline, having lost the contact to the simple yet deeply rooted questions which physics provided until the beginning of this century. We argue that, in contrary, there are indications that string theory might be linked to a fundamental principle of a quantum computational character. In addition, the nature of this principle can possibly provide some new insight into the question of universality of string theory (string theory as the “theory of everything”).     

Gödel's universe in a Supertube shroud

We demonstrate that certain supersymmetric G?del-like universe solutions of supergravity are not solutions of string theory. This is achieved by realizing that supertubes are Bogomol'nyi-Prasad-Sommerfeld states in these spaces, and under certain conditions, when wrapping closed timelike curves, some world-volume modes develop negative kinetic terms. Since these universes are homogeneous, this instability takes place everywhere in space-time. We also construct a family of supergravity solutions which locally look like the G?del universe inside a domain wall made out of supertubes, but have very different asymptotic structure. One can adjust the volume inside the domain wall so there will be no closed timelike curves, and then those spaces seem like perfectly good string backgrounds.     

Quantum Gravity and Phenomenological Philosophy

The central thesis of this paper is that contemporary theoretical physics is grounded in philosophical presuppositions that make it difficult to effectively address the problems of subject-object interaction and discontinuity inherent to quantum gravity. The core objectivist assumption implicit in relativity theory and quantum mechanics is uncovered and we see that, in string theory, this assumption leads into contradiction. To address this challenge, a new philosophical foundation is proposed based on the phenomenology of Maurice Merleau-Ponty and Martin Heidegger. Then, through the application of qualitative topology and hypernumbers, phenomenological ideas about space, time, and dimension are brought into focus so as to provide specific solutions to the problems of force-field generation and unification. The phenomenological string theory that results speaks to the inconclusiveness of conventional string theory and resolves its core contradiction. This article is based on my 2008 book, The Self-Evolving Cosmos, appearing in the Series on Knots and Everything of World Scientific Publishing Company.     

What we learn on the heterotic string vacua from anomaly-free supergravity

The recently constructed D = 10 anomaly-free supergravity (AFS) has been argued to contain the full effective theory of the heterotic string. The solutions of the effective theory must be solutions of AFS, while the converse is not necessarily true since string theory might specify the boundary conditions for the AFS torsion equation. We show that Calabi-Yau spaces are exact solutions of AFS, while compact group and coset manifolds are not. This is due to a positivity argument, which is the extension to anomaly-free supergravity of the “ten into four won't go” theorem of Freedman, Gibbons and West for the Chapline-Manton theory.     

Wilson loops T-dual to short strings

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near-BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincaré patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincaré horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual (“momentum”) theory.     

Gauge coupling unification in realistic free-fermionic string models

We discuss the unification of gauge couplings within the framework of a wide class of realistic free-fermionic string models which have appeared in the literature, including the flipped SU(5), SO(6) × SO(4), and various SU(3) × SU(2) × U(1) models. If the matter spectrum below the string scale is that of the Minimal Supersymmetric Standard Model (MSSM), then string unification is in disagreement with experiment. We therefore examine several effects that may modify the minimal string predictions. First, we develop a systematic procedure for evaluating the one-loop heavy string threshold corrections in free-fermionic string models, and we explicitly evaluate these corrections for each of the realistic models. We find that these string threshold corrections are small, and we provide general arguments explaining why such threshold corrections are suppressed in string theory. Thus heavy thresholds cannot resolve the disagreement with experiment. We also study the effect of non-standard hypercharge normalizations, light SUSY thresholds, and intermediate-scale gauge structure, and similarly conclude that these effects cannot resolve the disagreement with low-energy data. Finally, we examine the effects of additional color triplets and electroweak doublets beyond the MSSM. Although not required in ordinary grand unification scenarios, such states generically appear within the context of certain realistic free-fermionic string models. We show that if these states exist at the appropriate thresholds, then the gauge couplings will indeed unify at the string scale. Thus, within these string models, string unification can be in agreement with low-energy data.     

Meeting the constraint of neutrino—Higgsino mixing in gravity unified theories

In gravity unified theories all operators that are consistent with the local gauge and discrete symmetries are expected to arise in the effective low-energy theory. Given the absence of multiplets like 126 of SO(10) in string models, and assuming that B - L is violated spontaneously to generate light neutrino masses via a seesaw mechanism, it is observed that string theory solutions generically face the problem of producing an excessive mixing mass at the GUT scale, which is some nineteen orders of magnitude larger than the experimental bound of 1 MeV. The suppression of mixing, like proton longevity, thus provides one of the most severe constraints on the validity of any string theory solution. We examine this problem in a class of superstring derived models. We find a family of solutions within this class for which the symmetries of the models and an allowed pattern of VEVs, surprisingly, succeed in adequately suppressing the neutrino-Higgsino mixing terms. At the same time they produce the terms required to generate small neutrino masses via a seesaw mechanism.     

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.     

Vorton existence and stability

We present the first concrete evidence for the classical stability of vortons, circular cosmic string loops stabilized by the angular momentum of the charge and current trapped on the string. We begin by summarizing what is known about vorton solutions and, in particular, their analytic stability with respect to a range of radial and nonradial perturbations. We then discuss numerical results of vorton simulations in a full 3D field theory, that is, Witten's original bosonic superconducting string model with a modified potential term. For specific parameter values, these simulations demonstrate the long-term stability of sufficiently large vorton solutions created with an elliptical initial ansatz.     

Prolegomena to a theory of bifurcating universes: A nonlocal solution to the cosmological constant problem or little lambda goes back to the future

We outline a framework for describing the bifurcation of the universe into disconnected pieces, and formulate criteria for a system in which such phenomena occur, to describe local quantum physics in a single connected universe. The formalism is a four-dimensional analog of string field theory which we call Universal Field Theory (UFT). We argue that local dynamics in a single universe is a good approximation to UFT if the universal field is classical and if the vertex for emission of a new connected component of the universe is concentrated on universes of small volume. We show that classical UFT is equivalent to a Wheeler-DeWitt equation for a single connected universe plus a set of nonlocal gap equations for the couplings in the spacetime lagrangian. The effective action must be stationary with respect to the couplings. Nonlicality shoes up only at short distances. We solve the equation for the low-energy cosmological constant and show that if the universe undergoes substantial inflation then the cosmological constant is determined to be negative and very small. Its precise value may depend on the fate of nonrelativistic matter in the very late stages of universal expansion. Finally, we argue that corrections to the classical UFT are nonlocal and must be suppressed if the theory is to make sense. This may be the reason that supersymmetric vacua of string theory are not realized in nature.     

Extremal black holes as fundamental strings

We show that polarization-dependent string-string scattering provides new evidence for the identification of the Dabholkar-Harvey (DH) string solution with the heterotic string itself. First, we construct excited versions of the DH solution which carry arbitrary left-moving waves yet are annihilated by half the supersymmetries. These solutions correspond in a natural way to Bogomolny-bound-saturating excitations of the ground state of the heterotic string. When the excited string solutions are compactified to four dimensions, they reduce to Sen's family of extremal black hole solutions of the toroidally compactified heterotic string. We then study the large impact parameter scattering of two such string solutions. We develop methods which go beyond the metric on moduli space approximation and allow us to read off the subleading polarization-dependent scattering amplitudes. We find perfect agreement with heterotic string tree amplitude predictions for the scattering of corresponding string states. Taken together, these results clearly identify the string states responsible for Sen's extremal black hole entropy. We end with a brief discussion of implications for the black hole information problem.     

Nonlocal instantons and solitons in string models

We study a class of nonlocal systems which can be described by a local scalar field diffusing in an auxiliary radial dimension. As examples p-adic, open and boundary string field theory are considered on Minkowski, Friedmann–Robertson–Walker and Euclidean metric backgrounds. Starting from distribution-like initial field configurations which are constant almost everywhere, we construct exact and approximate nonlocal solutions. The Euclidean p-adic lump is interpreted as a solitonic brane, and the Euclidean kink of supersymmetric open string field theory as an instanton. Some relations between solutions of different string theories are highlighted also thanks to a reformulation of nonlocal systems as fixed points in a renormalization group flow.     

What is the magnetic Weak Gravity Conjecture for axions?

The electric Weak Gravity Conjecture demands that axions with large decay constant f couple to light instantons. The resulting large instantonic corrections pose problems for natural inflation. We explore an alternative argument based on the magnetic Weak Gravity Conjecture for axions, which we try to make more precise. Roughly speaking, it demands that the minimally charged string coupled to the dual 2‐form‐field exists in the effective theory. Most naively, such large‐f strings curve space too much to exist as static solutions, thus ruling out large‐f axions. More conservatively, one might allow non‐static string solutions to play the role of the required charged objects. In this case, topological inflation would save the superplanckian axion. Furthermore, a large‐f axion may appear in the low‐energy effective theory based on two subplanckian axions in the UV. The resulting effective string is a composite object built from several elementary strings and domain walls. It may or may not satisfy the magnetic Weak Gravity Conjecture depending on how strictly the latter is interpreted and on the cosmological dynamics of this composite object, which remain to be fully understood. Finally, we recall that large‐field brane inflation is naively possible in the codimension‐one case. We show how string‐theoretic back‐reaction closes this apparent loophole of large‐f (non‐periodic) pseudo‐axions.     

Standard model with partial gauge invariance

We study cosmological solutions in the effective heterotic string theory with ????-correction terms in the string frame. It is pointed out that the effective theory has an ambiguity via field redefinition and we analyze generalized effective theories due to this ambiguity. We restrict our analysis to the effective theories which give equations of motion of second order in the derivatives, just as ??Galileon?? field theory. This class of effective actions contains two free coupling constants. We find de Sitter solutions as well as the power-law expanding universes in our four-dimensional Einstein frame. The accelerated expanding universes are always attractors in the present dynamical system.     

Homotopy algebra morphism and geometry of classical string field theories

We discuss general properties of classical string field theories with symmetric vertices in the context of deformation theory. For a given conformal background, there are many string field theories corresponding to different decomposition of moduli space of Riemann surfaces. It is shown that any classical open string field theories on a fixed conformal background are A_∞-quasi-isomorphic to each other. This indicates that they have isomorphic moduli space of classical solutions. The minimal model theorem in A_∞-algebras plays a key role in these results. Its natural and geometric realization on formal supermanifolds is also given. The same results hold for classical closed string field theories, whose algebraic structures are governed by L_∞-algebras.     

Charting the landscape of supercritical string theory

Special solutions of string theory in supercritical dimensions can interpolate in time between theories with different numbers of spacetime dimensions and different amounts of world sheet supersymmetry. These solutions connect supercritical string theories to the more familiar string duality web in ten dimensions and provide a precise link between supersymmetric and purely bosonic string theories. Dimension quenching and c duality appear to be natural concepts in string theory, giving rise to large networks of interconnected theories.