Conference

It is widely held that string theory shows that spacetime geometry and topology are emergent rather than fundamental. Often it is said that this follows from the various interesting dualities that exist within string theory. I will discuss the argument from duality, contrasting it with older arguments for the non-objectivity of spatiotemporal topology. I hope that this will clarify some questions about the role of spacetime in string theory---and about the differences between the ways that philosophers and physicists approach these questions.

Our ability to understand the physical world has to a large extent depended on the existence of emergent properties, and the separation of scales that permits effective field theory descriptions to be useful. Exploiting this fact, we can construct minimal models that enable efficient calculation of desired quantities, as long as they are insensitive to microscopic details. This works in many instances in physics, and I give some examples drawn from the kinetics of phase transitions mediated by topological defects. In other fields, such as biology, it is not so clear that these concepts are useful, and I will discuss to what extent emergence and effective theories might be useful.

This talk considers the extent to which the intertheoretic relation between an EFT and its (possibly hypothetical) high-energy theory supports a notion of emergence. When a high-energy theory exists, this relation is based on a process that involves the elimination of high-energy degrees of freedom. This elimination results in an EFT that formally bears little resemblance to the high-energy theory. I investigate the extent to which this lack of formal resemblance underwrites notions of novelty and autonomy that may be appropriately associated with emergence. I'll begin by reviewing the method by which an EFT is constructed from a high-energy theory by means of integrating out high-energy degrees of freedom from the latter. I'll then review a number of attempts in the philosophical literature to explicate the notion of emergence. I'll first consider general phillosophical accounts that identify emergence as supervienience without reduction, or as associated with various notions of autonomy (reductive, predictive, causal, and/or explanatory). I'll then consider more specific accounts related to physics in particular, including Batterman's (2002) notion of the failure of a limiting relation, and Mainwood's (2006)description of the concept of emergence associated with the claims of condensed matter physicists (e.g., Anderson 1972). This account conceives emergence as microphysicalism (the claim that emergent properties/entities are ultimately composed of microphysical properties/entities) coupled with novelty cashed out in terms of a mechanism (in this case spontaneous symmetry breaking) that produces a reduced phase space supporting (emergent) properties that are not explicitly defined on the initial phase space. A similar account is given by Wilson (2010), who explicates novelty in terms of an elimination of degrees of freedom. I'll suggest that Batterman's account does not quite succeed in the context of EFTs (simply put, the relation between an EFT and its high-energy theory cannot be described in terms of the failure of a limiting relation), and while the elimination of degrees of freedom does occur in EFTs, this process is different from the process described by Mainwood and Wilson (in particular, the phase space of an EFT is not, in general, a reduced phase space of a high-energy theory). This suggests that a notion of emergence as microphysicalism coupled with novelty can be applicable to the EFT context, as long as an appropriate mechanism that underwrites novelty, other than spontaneous symmetry breaking, can be identified. This mechanism perhaps can be identified simply as the particular approximation scheme employed in the construction of an EFT.

In the philosophical literature, effective field theories have been regarded as emergent in the sense of furnishing novel explanations. In particular, Batterman has argued that effective field theories in statistical mechanics are emergent in this sense. I will argue that effective field theories in quantum field theory do not furnish analogous novel explanations. There are relevant disanalogies between statistical mechanics and quantum field theory with regard to the roles played by idealizations and the explanatory goals of the application of renormalization group methods. Contrasting the statistical mechanics and quantum field theory cases highlights the role that the physical interpretation of the formalism and the goals of theorizing play in determining whether a particular effective theory counts as emergent.

How can one model the behavior of materials that display radically different, dominant behaviors at different length scales. Although we have good models for material behaviors at small and large scales, it is often hard to relate these scale-based models to one another. Macroscale (effective) models represent the integrated effects of very subtle factors that are practically invisible at the smallest, atomic, scales. For this reason it has been notoriously difficult to model realistic materials with a simple bottom-up-from-the-atoms strategy. The widespread failure of that strategy forced physicists interested in overall macro-behavior of materials toward completely top-down modeling strategies familiar from traditional continuum mechanics. The problem of the ``tyranny of scales'' asks whether we can exploit our rather rich knowledge of intermediate micro- (or meso-) scale behaviors in a manner that would allow us to bridge between these two dominant methodologies. Macroscopic scale behaviors often fall into large common classes of behaviors such as the class of isotropic elastic solids, characterized by two phenomenological parameters---so-called elastic coefficients. Can we employ knowledge of lower scale behaviors to understand this universality---to determine the coefficients and to group the systems into classes exhibiting similar behavior?

In 1665, the clockmaker Christiaan Huygens noticed that two pendulum clocks hanging on a wall tend to synchronize the motion of their pendulums. A similar scenario occurs with two metronomes placed on a piano: they interact through vibrations in the wood and will eventually coordinate their motion. These effects are stable against small perturbations. Such stability is not predicted by either Hamiltonian mechanics or by few-body quantum theory. Nonetheless they can be seen as occurring within a simple model introduced by Kolmogorov. Surprisingly, this model leads to a very complex phase diagram. In turn, the complexities of this phase diagram have been observed within experimental observations of fluid flow, solid state devices, and non-linear electrical circuits. It is reflective of the structure of number theory and of the relation between rational and irrational numbers. Of course, the synchronization arises from friction, an effect often neglected in fundamental theories. Should we then regard synchronization, and its deeply mathematical explanation, as an example of an emergent phenomenon? What does emergence mean? Is is just something that surprises us? How are emergent phenomena connected with the fundamentals of our physical theories?

In this second presentation, we will revisit Feynman's first argument and discuss how it still strongly influences variational studies of relativistic field theories with MPS or cMPS. However, as we explain, this argument can be completely overcome by introducing different variational parameters for the different length scales in the system, a strategy that naturally results in the MERA for lattice systems, or its continuous version for field theories. We then illustrate how a cMERA representation for the ground state of free relativistic quantum field theories can be constructed and discuss the main properties of this representation.

In this talk I will describe how to generalize the multiscale entanglement renormalization ansatz to quantum fields. The resulting variational class of wavefunctions, cMERA, arising from this RG flow are translation invariant and exhibit an entropy-area law. I'll illustrate the construction for some example fields, and describe how to cover the case of interacting theories.

Topological Quantum field theories(TQFTs) are a special class of QFTs. Their actions do not depend on the metric of the background space-time manifold. Thus, it is very natural to define TQFTs on an arbitrary triangulation of the space-time manifold and they are independent on the triangulation. More importantly, TQFTs defined on triangulations are always a finite theory associated with a well defined cut-off. A well known example is the Turaev-Viro states sum invariants. Essentially, the Turaev-Viro constructions are (local) tensor network representations of a special class of 1+2D TQFTs. In this talk, I will show a new class of TQFTs that can be derived based on the (local) tensor network representations in arbitrary dimensions. They can be regarded as the discrete analogy of topological Berry phase terms of (discrete) non-linear sigma models. The edge theory of such a new class of TQFTs can be regarded as the discrete analogy of WZW terms. This new class of TQFTs naturally classify (bosonic) symmetry protected topological orders in arbitrary dimensions. Finally, I will also discuss new classes of fermionic TQFTs based on the Grassmann tensor network representations and possible new route towards Quantum Gravity(QG).

The MERA offers a powerful variational approach to quantum field theory. While the continuous MERA may allow us to directly address field theories in the continuum, the MERA on the lattice has already demonstrated its ability to characterize conformal field theories. In this talk I will explain how to extract the conformal data (central charge, primary fields, and their scaling dimensions and OPE) of a CFT from a quantum spin chain at a quantum critical point. I will consider both homogeneous systems (translation invariant) and systems with an impurity (where translation invariance is explicitly broken). Key to the success of the MERA is the exploitation of both scale and translation invariance. I will show how translation invariance can still be exploited even in the presence of an impurity, even if the system is no longer translation invariant. This follows from an intriguing "causality principle" in the RG flow. I will also discuss the relation of these results with Wilson's famous resolution of the Kondo impurity problem.

One might be confused by the proliferation of tensor network states, such as MPS, PEPS, tree tensor networks [TTN], MERA, etc. What is the main difference between them? In this talk I will argue that the geometry of a tensor network determines several properties of the state that is being represented, such as the asymptotic scaling of correlations and of entanglement entropy. I will also describe the relation between the MERA and the Renormalization Group, and will review Brian Swingle

In 1987, Feynman devoted one of his last lectures to highlighting three serious objections against the usefulness of the variational principle in the theory of relativistic quantum fields. In that same year, in a different branch of physics, Affleck, Kennedy, Lieb and Tasaki devised a quantum state that resulted in the development of a handful of different variational ansätze for lattice models over the last two decennia. These quantum states are known as tensor network states and invalidate at least two of Feynman's arguments. They could thus be used in a variational study of relativistic quantum field theories on a lattice. However, two classes of tensor network states, namely the matrix product state and the multi-scale entanglement renormalization ansatz, have recently been ported to the continuous setting, so that we now have direct access to variational wave functions for quantum field theories and are no longer restricted to a lattice regularization.