Search

Singularities in general relativity and quantum field theory are often taken not only to motivate the search for a more-fundamental theory (quantum gravity, QG), but also to characterise this new theory and shape expectations of what it is to achieve. Here, we first evaluate how particular types of singularities may suggest an incompleteness of current theories. We then classify four different ‘attitudes’ towards singularities in the search for QG, and show, through examples in the physics literature, that these lead to different scenarios for the new theory. Two of the attitudes prompt singularity resolution, but only one suggests the need for a theory of QG. Rather than evaluate the different attitudes, we close with some suggestions of factors that influence the choice between them.

I begin to develop a framework for emergence in the physical sciences. Namely, I propose to explicate ontological emergence in terms of the notion of 'novel reference', and of an account of interpretation as a map from theory to world. I then construe ontological emergence as the "failure of the interpretation to mesh" with an appropriate linkage map between theories. Ontological emergence can obtain between theories that have the same extension but different intensions, and between theories that have both different extensions and intensions. I illustrate the framework in three examples: the emergence of spontaneous magnetisation in a ferromagnet, the emergence of masslessness, and the emergence of space, in specific models of physics. The account explains why ontological emergence is independent of reduction: namely, because emergence is primarily concerned with adequate interpretation, while the sense of reduction that is relevant here is concerned with inter-theoretic relations between uninterpreted theories., Comment: 54 pages. Published version, references updated

Dualities offer new possibilities for relating fundamentality and emergence. In particular, as is the aim of this chapter to show, it may happen that the relations of fundamentality and emergence between dual theories are inverted. In other words, the direction of emergence typically found in these cases is opposite to the direction of emergence followed in the standard accounts: that is, while the standard emergence direction is that of decreasing fundamentality---in that there is emergence of less fundamental, high-level entities, out of more fundamental, low-level entities---in these cases of duality, on the contrary, a more fundamental entity can emerge out of a less fundamental one. In fact, this possibility can be traced back to the existence of different classical limits in quantum field theories and string theories.

We argue that gravity theories in AdS4 are holographically dual to either of two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton acts as a source for the stress-energy tensor, and a dual CFT2 with a fixed dual graviton which acts as a source for a dual stress-energy tensor. The dual stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The two CFT's are related by a Legendre transformation generated by a gravitational Chern-Simons coupling. This duality is a gravitational version of electric-magnetic duality valid at any radius r, where the renormalized stress-energy tensor is the electric field and the Cotton tensor is the magnetic field. Generic Robin boundary conditions lead to CFT's coupled to Cotton gravity or topologically massive gravity. Interaction terms with CFT1 lead to a non-zero vev of the stress-energy tensor in CFT2 coupled to gravity even after the source is removed. We point out that the dual graviton also exists beyond the linearized approximation, and spell out some of the details of the non-linear construction.

In this paper we present a schema for describing dualities between physical theories (Sections 2 and 3), and illustrate it in detail with the example of bosonization: a boson-fermion duality in two-dimensional quantum field theory (Sections 4 and 5). The schema develops proposals in De Haro (2016, 2016a): these proposals include construals of notions related to duality, like representation, model, symmetry and interpretation. The aim of the schema is to give a more precise criterion for duality than has so far been considered. The bosonization example, or boson-fermion duality, has the feature of being simple yet rich enough to illustrate the most relevant aspects of our schema, which also apply to more sophisticated dualities. The richness of the example consists, mainly, in its concern with two non-trivial quantum field theories: including massive Thirring-sine-Gordon duality, and non-abelian bosonization. This prompts two comparisons with the recent literature on dualities:--- (a) Unlike the standard cases of duality in quantum field theory and string theory, where only specific simplifying limits of the theories are explicitly known, the boson-fermion duality is known to hold exactly. This exactness can be exhibited explicitly. (b) The bosonization example illustrates both the cases of isomorphic and non-isomorphic models: which we believe the literature on dualities has not so far discussed.

Mutations in NBEAL2, the gene encoding the scaffolding protein Nbeal2 are causal of Gray Platelet Syndrome (GPS), a rare recessive bleeding disorder characterized by platelets lacking α-granules and progressive marrow fibrosis. We present here the interactome of Nbeal2 with additional validation by reverse immunoprecipitation of Dock7, Sec16a and Vac14 as interactors of Nbeal2. We show that GPS-causing mutations in its BEACH domain have profound and possible effects on the interaction with Dock7 and Vac14, respectively. Proximity ligation assays show that these two proteins are physically proximal to Nbeal2 in human megakaryocytes. In addition, we demonstrate that Nbeal2 is primarily localized in the cytoplasm and Dock7 on the membrane of or in α-granules. Interestingly, platelets from GPS cases and Nbeal2-/- mice are almost devoid of Dock7 resulting in a profound dysregulation of its signaling pathway, leading to defective actin polymerization, platelet activation and shape change. This study shows for the first time proteins interacting with Nbeal2 and points to the dysregulation of the canonical signaling pathway of Dock7 as a possible cause of the aberrant formation of platelets in GPS cases and Nbeal2 deficient mice.

The history of string theory started around 1970 when Nambu, Nielsen, and Susskind realized that Veneziano’s 1968 dual model, devised to explain the particle spectrum of the strong interactions, actually describes the properties of quantum mechanical strings. A few years later, QCD appeared as a superior model for the strong interactions; furthermore, in 1974 it was realized that strings contain gravitons in their spectrum. For these reasons, many lost interest in the theory, while for some it made an interesting candidate as a unifying theory of gravity and quantum field theory.

We argue that gravity theories in AdS4 are holographically dual to either of two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton acts as a source for the stress-energy tensor, and a dual CFT2 with a fixed dual graviton which acts as a source for a dual stress-energy tensor. The dual stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The two CFT's are related by a Legendre transformation generated by a gravitational Chern-Simons coupling. This duality is a gravitational version of electric-magnetic duality valid at any radius r, where the renormalized stress-energy tensor is the electric field and the Cotton tensor is the magnetic field. Generic Robin boundary conditions lead to CFT's coupled to Cotton gravity or topologically massive gravity. Interaction terms with CFT1 lead to a non-zero vev of the stress-energy tensor in CFT2 coupled to gravity even after the source is removed. We point out that the dual graviton also exists beyond the linearized approximation, and spell out some of the details of the non-linear construction.

We compute expectation values of Wilson loops in q-deformed 2d Yang-Mills on a Riemann surface and show that they give invariants of knots in 3-manifolds which are circle bundles over the Riemann surface. The areas of the loops play an essential role in encoding topological information about the extra dimension, and they are quantized to integer or half integer values.

We discuss the computation of the leading corrections to D-brane solutions due to higher derivative terms in the corresponding low energy effective action. We develop several alternative methods for analyzing the problem. In particular, we derive an effective one-dimensional action from which the field equations for spherically symmetric two-block brane solutions can be derived, show how to obtain first order equations, and discuss a few other approaches. We integrate the equations for extremal branes and obtain the corrections in terms of integrals of the evaluation of the higher derivative terms on the lowest order solution. To obtain completely explicit results one would need to know all leading higher derivative corrections which at present are not available. One of the known higher derivative terms is the R^4 term, and we obtain the corrections to the D3 brane solution due to this term alone. We note, however, that (unknown at present) higher terms depending on F_5 are expected to modify our result. We analyze the thermodynamics of brane solutions when such quantum corrections are present. We find that the R^4 term induces a correction to the tension and the electric potential of the D3 brane but not to its charge, and the tension is still proportional to the electric potential times the charge. In the near-horizon limit the corrected solution becomes AdS_5 \times S^5 with the same cosmological constant as the lowest order solution but a different value of the (constant) dilaton., 37 pages, v2: PRD version

We analyze the possibility of constructing a supersymmetric invariant that contains the $R^4$ term among its components as a superpotential term in type IIB on-shell superspace. We consider a scalar superpotential, i.e. an arbitrary holomorphic function of a chiral scalar superfield. In general, IIB superspace does not allow for the existence of chiral superfields, but the obstruction vanishes for a specific superfield, the dilaton superfield. This superfield contains all fields of type IIB supergravity among its components, and its existence is implied by the solution of the Bianchi identities. The construction requires the existence of an appropriate chiral measure, and we find an obstruction to the existence of such a measure. The obstruction is closely related to the obstruction for the existence of chiral superfields and is non-linear in the fields. These results imply that the IIB superinvariant related to the $R^4$ term is not associated with a scalar chiral superpotential., Comment: 43 pages, v3: version to appear in PRD

Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the Schema. This construal entails interpretative constraints that should be useful for theoretical equivalence more generally. I illustrate the construal in various formulations of Maxwell's electromagnetic theory., 43 pages

Funder: Trinity College, University of Cambridge; doi: http://dx.doi.org/10.13039/501100000727, In this paper I review the problematic relationship between science and philosophy; in particular, I will address the question of whether science needs philosophy, and I will offer some positive perspectives that should be helpful in developing a synergetic relationship between the two. I will review three lines of reasoning often employed in arguing that philosophy is useless for science: (a) philosophy’s death diagnosis (‘philosophy is dead’); (b) the historic-agnostic argument/challenge “show me examples where philosophy has been useful for science, for I don’t know of any”; (c) the division of property argument (or: philosophy and science have different subject matters, therefore philosophy is useless for science). These arguments will be countered with three contentions to the effect that the natural sciences need philosophy. I will: (a) point to the fallacy of anti-philosophicalism (or: ‘in order to deny the need for philosophy, one must do philosophy’) and examine the role of paradigms and presuppositions (or: why science can’t live without philosophy); (b) point out why the historical argument fails (in an example from quantum mechanics, alive and kicking); (c) briefly sketch some domains of intersection of science and philosophy and how the two can have mutual synergy. I will conclude with some implications of this synergetic relationship between science and philosophy for the liberal arts and sciences.

While the relation between visualization and scientific understanding has been a topic of long-standing discussion, recent developments in physics have pushed the boundaries of this debate to new and still unexplored realms. For it is claimed that, in certain theories of quantum gravity, spacetime 'disappears': and this suggests that one may have sensible physical theories in which spacetime is completely absent. This makes the philosophical question whether such theories are intelligible, even more pressing. And if such theories are intelligible, the question then is how they manage to do so. In this paper, we adapt the contextual theory of scientific understanding, developed by one of us, to fit the novel challenges posed by physical theories without spacetime. We construe understanding as a matter of skill rather than just knowledge. The appeal is thus to understanding, rather than explanation, because we will be concerned with the tools that scientists have at their disposal for understanding these theories. Our central thesis is that such physical theories can provide scientific understanding, and that such understanding does not require spacetimes of any sort. Our argument consists of four consecutive steps: (a) We argue, from the general theory of scientific understanding, that although visualization is an oft-used tool for understanding, it is not a necessary condition for it; (b) we criticise certain metaphysical preconceptions which can stand in the way of recognising how intelligibility without spacetime can be had; (c) we catalogue tools for rendering theories without a spacetime intelligible; and (d) we give examples of cases in which understanding is attained without a spacetime, and explain what kind of understanding these examples provide., 28 pages, forthcoming in Synthese

I conceptualise the role of dualities in quantum gravity, in terms of their functions for theory construction. I distinguish between two functions of duality in physical practice: namely, discovering and describing 'equivalent physics', vs. suggesting 'new physics'. I dub these the 'theoretical' vs. the 'heuristic' functions of dualities. The distinction seems to have gone largely unnoticed in the philosophical literature: and it exists both for dualities, and for the more general relation of theoretical equivalence. The paper develops the heuristic function of dualities: illustrating how they can be used, if one has any luck, to find and formulate new theories. I also point to the different physical commitments about the theories in question that underlie these two functions. I show how a recently developed schema for dualities articulates the differences between the two functions., Comment: 37 pages. v2: references updated, published version

I examine the relationship between (d+1)-dimensional Poincaré metrics and d-dimensional conformal manifolds, from both mathematical and physical perspectives. The results have a bearing on several conceptual issues relating to asymptotic symmetries, in general relativity and in gauge-gravity duality, as follows: (1: Ambient Construction) I draw from the remarkable work by Fefferman and Graham (1985, 2012) on conformal geometry, in order to prove two propositions and a theorem that characterise the classes of diffeomorphisms that qualify as {\it gravity-invisible}. I define natural notions of gravity-invisibility (strong, weak, and simpliciter) which apply to the diffeomorphisms of Poincaré metrics in any dimension. (2: Dualities) I apply the notions of invisibility to gauge-gravity dualities: which, roughly, relate Poincaré metrics in d+1 dimensions to QFTs in d dimensions. I contrast {\it QFT-visible} vs. {\it QFT-invisible} diffeomorphisms: those gravity diffeomorphisms that can, respectively cannot, be seen from the QFT. The QFT-invisible diffeomorphisms are the ones which are relevant to the hole argument in Einstein spaces. The results on dualities are surprising, because the class of QFT-visible diffeomorphisms is {\it larger} than expected, and the class of QFT-invisible ones is {\it smaller} than expected, or usually believed, i.e. larger than the PBH diffeomorphisms in Imbimbo et al. (2000). I also give a general derivation of the asymptotic conformal Killing equation, which has not appeared in the literature before., This work was supported by the Tarner scholarship in Philosophy of Science and History of Ideas, held at Trinity College, Cambridge.

Funder: Trinity College, University of Cambridge; doi: http://dx.doi.org/10.13039/501100000727, We advocate an account of dualities between physical theories: the basic idea is that dual theories are isomorphic representations of a common core. We defend and illustrate this account, which we call a Schema, in relation to symmetries. Overall, the account meshes well with standard treatments of symmetries. But the distinction between the common core and the dual theories prompts a distinction between three kinds of symmetry: which we call ‘stipulated’, ‘accidental’ and ‘proper’.