arXiv subjects

Timothy J. Hollowood

Publications and source records attributed to Timothy J. Hollowood.

At least 37 records · Page 2Linked to original sources

arXiv2016

Causality, Renormalizability and Ultra-High Energy Gravitational Scattering

The amplitude A(s,t) for ultra-high energy scattering can be found in the leading eikonal approximation by considering propagation in an Aichelburg-Sexl gravitational shockwave background. Loop corrections in the QFT describing the scattered particles are encoded for energies below the Planck scale in an effective action which in general exhibits causality violation and Shapiro time advances. In this paper, we use Penrose limit techniques to calculate the full energy dependence of the scattering phase shift Theta_scat(hat_s},, where the single variable hat_s = Gs/m^2 b^(d-2) contains both the CM energy s and impact parameter b, for a range of scalar QFTs in d dimensions with different renormalizability properties. We evaluate the high-energy limit of Theta_scat(hat_s) and show in detail how causality is related to the existence of a well-defined UV completion. Similarities with graviton scattering and the corresponding resolution of causality violation in the effective action by string theory are briefly discussed.

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arXiv2016

Causality Violation, Gravitational Shockwaves and UV Completion

The effective actions describing the low-energy dynamics of QFTs involving gravity generically exhibit causality violations. These may take the form of superluminal propagation or Shapiro time advances and allow the construction of "time machines", i.e. spacetimes admitting closed non-spacelike curves. Here, we discuss critically whether such causality violations may be used as a criterion to identify unphysical effective actions or whether, and how, causality problems may be resolved by embedding the action in a fundamental, UV complete QFT. We study in detail the case of photon scattering in an Aichelburg-Sexl gravitational shockwave background and calculate the phase shifts in QED for all energies, demonstrating their smooth interpolation from the causality-violating effective action values at low-energy to their manifestly causal high-energy limits. At low energies, these phase shifts may be interpreted as backwards-in-time coordinate jumps as the photon encounters the shock wavefront, and we illustrate how the resulting causality problems emerge and are resolved in a two-shockwave time machine scenario. The implications of our results for ultra-high (Planck) energy scattering, in which graviton exchange is modelled by the shockwave background, are highlighted.

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arXiv2015

Partition function of N=2* SYM on a large four-sphere

We examine the partition function of N=2* supersymmetric SU(N) Yang-Mills theory on the four-sphere in the large radius limit. We point out that the large radius partition function, at fixed N, is computed by saddle points lying on particular walls of marginal stability on the Coulomb branch of the theory on R^4. For N an even (odd) integer and θ_YM=0, (π), these include a point of maximal degeneration of the Donagi-Witten curve to a torus where BPS dyons with electric charge [N/2] become massless. We argue that the dyon singularity is the lone saddle point in the SU(2) theory, while for SU(N) with N>2, we characterize potentially competing saddle points by obtaining the relations between the Seiberg-Witten periods at such points. Using Nekrasov's instanton partition function, we solve for the maximally degenerate saddle point and obtain its free energy as a function of g_YM and N, and show that the results are "large-N exact". In the large-N theory our results provide analytical expressions for the periods/eigenvalues at the maximally degenerate saddle point, precisely matching previously known formulae following from the correspondence between N=2* theory and the elliptic Calogero-Moser integrable model. The maximally singular point ceases to be a saddle point of the partition function above a critical value of the coupling, in agreement with the recent findings of Russo and Zarembo.

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arXiv2015

Copenhagen Quantum Mechanics

In our quantum mechanics courses, measurement is usually taught in passing, as an ad-hoc procedure involving the ugly collapse of the wave function. No wonder we search for more satisfying alternatives to the Copenhagen interpretation. But this overlooks the fact that the approach fits very well with modern measurement theory with its notions of the conditioned state and quantum trajectory. In addition, what we know of as the Copenhagen interpretation is a later 1950's development and some of the earlier pioneers like Bohr did not talk of wave function collapse. In fact, if one takes these earlier ideas and mixes them with later insights of decoherence, a much more satisfying version of Copenhagen quantum mechanics emerges, one for which the collapse of the wave function is seen to be a harmless book keeping device. Along the way, we explain why chaotic systems lead to wave functions that spread out quickly on macroscopic scales implying that Schrodinger cat states are the norm rather than curiosities generated in physicists' laboratories. We then describe how the conditioned state of a quantum system depends crucially on how the system is monitored illustrating this with the example of a decaying atom monitored with a time of arrival photon detector, leading to Bohr's quantum jumps. On the other hand, other kinds of detection lead to much smoother behaviour, providing yet another example of complementarity. Finally we explain how classical behaviour emerges, including classical mechanics but also thermodynamics.

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arXiv2015

Beta Function of k Deformed AdS_5 x S^5 String Theory

We calculate the one loop beta function for the would-be marginal coupling on the world sheet of the k deformed sigma models associated to a quantum group with q=exp(i pi/k). This includes the bosonic principal chiral models and symmetric space sigma models but also the k deformed semi-symmetric space sigma model describing strings in a deformation of AdS_5 x S^5. The world sheet sigma model is a current-current deformation of the gauged WZW model for the supergroup PSU(2,2|4) with level k. In the string theory context the beta function is shown to vanish because of the vanishing of the Killing form of PSU(2,2|4) which is another piece of evidence that the k deformed theories define consistent string theories.

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arXiv2015

S-Matrices and Quantum Group Symmetry of k-Deformed Sigma Models

Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with q=exp(i pi/k) a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.

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arXiv2015

The Copenhagen Interpretation Born Again

An approach to quantum mechanics is developed which makes the Heisenberg cut between the deterministic microscopic quantum world and the partly deterministic, partly stochastic macroscopic world explicit. The microscopic system evolves according to the Schrodinger equation with stochastic behaviour arising when the system is probed by a set of coarse grained macroscopic observables whose resolution scale defines the Heisenberg cut. The resulting stochastic process can account for the different facets of the classical limit: Newton's laws (ergodicity broken); statistical mechanics of thermal ensembles (ergodic); and solve the measurement problem (partial ergodicity breaking). In particular, the usual rules of the Copenhagen interpretation, like the Born rule, emerge, along with completely local descriptions of EPR type experiments. The formalism also re-introduces a dynamical picture of equilibration and thermalization in quantum statistical mechanics and provides insight into how classical statistical mechanics can arise in the classical limit and in a way that alleviates various conceptual problems.

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arXiv2014

An Integrable Deformation of the AdS5 x S5 Superstring

The S-matrix on the world-sheet theory of the string in AdS5 x S5 has previously been shown to admit a deformation where the symmetry algebra is replaced by the associated quantum group. The case where q is real has been identified as a particular deformation of the Green-Schwarz sigma model. An interpretation of the case with q a root of unity has, until now, been lacking. We show that the Green-Schwarz sigma model admits a discrete deformation which can be viewed as a rather simple deformation of the F/F_V gauged WZW model, where F=PSU(2,2|4). The deformation parameter q is then a k-th root of unity where k is the level. The deformed theory has the same equations-of-motion as the Green-Schwarz sigma model but has a different symplectic structure. We show that the resulting theory is integrable and has just the right amount of kappa-symmetries that appear as a remnant of the fermionic part of the original gauge symmetry. This points to the existence of a fully consistent deformed string background.

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arXiv2014

Integrable Deformations of Strings on Symmetric Spaces

A general class of deformations of integrable sigma-models with symmetric space F/G target-spaces are found. These deformations involve defining the non-abelian T dual of the sigma-model and then replacing the coupling of the Lagrange multiplier imposing flatness with a gauged F/F WZW model. The original sigma-model is obtained in the limit of large level. The resulting deformed theories are shown to preserve both integrability and the equations-of-motion, but involve a deformation of the symplectic structure. It is shown that this deformed symplectic structure involves a linear combination of the original Poisson bracket and a generalization of the Faddeev-Reshetikhin Poisson bracket which we show can be re-expressed as two decoupled F current algebras. It is then shown that the deformation can be incorporated into the classical model of strings on R x F/G via a generalization of the Pohlmeyer reduction. In this case, in the limit of large sigma-model coupling it is shown that the theory becomes the relativistic symmetric space sine-Gordon theory. These results point to the existence of a deformation of this kind for the full Green-Schwarz superstring on AdS5 x S5.

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arXiv2014

Schrodinger's Cat and the Firewall

It has been argued that when black holes are treated as quantum systems there are implications at the horizon and not just the singularity. Infalling observers will meet a firewall of high energy quanta. We argue that the question of whether an observer falling into a black hole experiences a smooth horizon or a firewall is identical to the question of whether Schrodinger's cat is either in a definite state, alive or dead, or in a superposition of the two. Since experience with real macro-systems indicate the former, the black hole state vector is seen to describe a set of decoherent alternatives each with a smooth horizon and the entanglement puzzle is thereby side stepped.

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arXiv2014

Symplectic Deformations of Integrable Field Theories and AdS/CFT

Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical level. The latter hierarchy admits a family of symplectic structures which we argue can be viewed as deformations of the relativistic sine-Gordon symplectic structure. These deformed theories are integrable but no longer relativistic and the basic excitations of the theory, the solitons, have an interesting non-relativistic dispersion relation that in a certain limit becomes the dispersion relation of dyonic giant magnons of string theory in the AdS/CFT correspondence. We argue that the deformed classical theories can be lifted to quantum theories when the sine-Gordon theory is embedded in a larger theory that describes the string world-sheet sigma model in AdS(5)xS(5).

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arXiv2013

New Modal Quantum Mechanics

We describe an interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description for macro-systems. The interpretation is a modal one, but does not suffer from the range of problems that plague other modal interpretations. The key feature is that quantum states carry an additional property assignment in the form of one the eigenvectors of the reduced density matrix which evolves evolves according to a stochastic process driven by the unmodified Schrodinger equation, but it is usually hidden from the emergent classical description due to the ergodic nature of its dynamics. However, during a quantum measurement, ergodicity is broken by decoherence and definite outcomes occur with probabilities that agree with the Born rule.

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arXiv2013

The Emergent Copenhagen Interpretation of Quantum Mechanics

We introduce a new and conceptually simple interpretation of quantum mechanics based on reduced density matrices of sub-systems from which the standard Copenhagen interpretation emerges as an effective description of macroscopically large systems. Wave function collapse is seen to be a useful but fundamentally unnecessary piece of prudent book keeping which is only valid for macro-systems. The new interpretation lies in a class of modal interpretations in that it applies to quantum systems that interact with a much larger environment. However, we show that it does not suffer from the problems that have plagued similar modal interpretations like macroscopic superpositions and rapid flipping between macroscopically distinct states. We describe how the interpretation fits neatly together with fully quantum formulations of statistical mechanics and that a measurement process can be viewed as a process of ergodicity breaking analogous to a phase transition. The key feature of the new interpretation is that joint probabilities for the ergodic subsets of states of disjoint macro-systems only arise as emergent quantities. Finally we give an account of the EPR-Bohm thought experiment and show that the interpretation implies the violation of the Bell inequality characteristic of quantum mechanics but in a way that is rather novel. The final conclusion is that the Copenhagen interpretation gives a completely satisfactory phenomenology of macro-systems interacting with micro-systems.

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arXiv2013

Asymptotic symmetries and thermodynamics of higher spin black holes in AdS3

We study black holes carrying higher spin charge in AdS3 within the framework of SL(N, R) x SL(N, R) Chern-Simons theory. Focussing attention on the N=4 case, we explicitly analyze the asymptotic symmetry algebra of black hole solutions with a chemical potential for spin-four charge. We demonstrate that the background describes an RG flow between an IR fixed point with W_4 symmetry and a UV fixed point with W-symmetry associated to a non-principal embedding of sl(2) in sl(4). Matching Chern-Simons equations with Ward identities of the deformed CFT, we show that the UV stress tensor is twisted by a certain U(1) current, and the flow is triggered by an operator with dimension 4/3 at the UV fixed point. We find independent confirmation of this picture via a consistent formulation of thermodynamics with respect to this UV fixed point. We further analyze the thermodynamics of multiple branches of black hole solutions for N=4,5 and find that the BTZ-branch, dominant at low temperatures, ceases to exist at higher temperatures following a merger with a thermodynamically unstable branch. We also point out an interesting connection between the RG flows and generalized KdV hierarchies.

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arXiv2013

Restoring Unitarity in the q-Deformed World-Sheet S-Matrix

The world-sheet S-matrix of the string in AdS5 x S5 has been shown to admit a q-deformation that relates it to the S-matrix of a generalization of the sine-Gordon theory, which arises as the Pohlmeyer reduction of the superstring. Whilst this is a fascinating development the resulting S-matrix is not explicitly unitary. The problem has been known for a long time in the context of S-matrices related to quantum groups. A braiding relation often called "unitarity" actually only corresponds to quantum field theory unitarity when the S-matrix is Hermitian analytic and quantum group S-matrices manifestly violate this. On the other hand, overall consistency of the S-matrix under the bootstrap requires that the deformation parameter is a root of unity and consequently one is forced to perform the "vertex" to IRF, or SOS, transformation on the states to truncate the spectrum consistently. In the IRF formulation unitarity is now manifest and the string S-matrix and the S-matrix of the generalised sine-Gordon theory are recovered in two different limits. In the latter case, expanding the Yang-Baxter equation we find that the tree-level S-matrix of the Pohlmeyer-reduced string should satisfy a modified classical Yang-Baxter equation explaining the apparent anomaly in the perturbative computation. We show that the IRF form of the S-matrix meshes perfectly with the bootstrap equations.

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arXiv2013

The Structure of Non-Abelian Kinks

We consider a class of integrable quantum field theories in 1+1 dimensions whose classical equations have kink solutions with internal collective coordinates that transform under a non-abelian symmetry group. These generalised sine-Gordon theories have been shown to be related to the world sheet theory of the string in the AdS/CFT correspondence. We provide a careful analysis of the boundary conditions at spatial infinity complicated by the fact that they are defined by actions with a WZ term. We go on to describe the local and non-local charges carried by the kinks and end by showing that their structure is perfectly consistent with the exact factorizable S-matrices that have been proposed to describe these theories.

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arXiv2013

The Copenhagen Interpretation as an Emergent Phenomenon

The Copenhagen interpretation has been remarkably successful but seems at odds with the underlying linearity of quantum mechanics. We show how it can emerge in a simple way from the underlying microscopic quantum world governed by Schrodinger's equation without the need for observers or their brains. In order to achieve this, we assemble pieces of various pre-existing ideas. Firstly, we adopt a relational approach and use the eigenvectors of the reduced density matrix of a quantum sub-system, or equivalently the Schmidt decomposition, to define the `internal state' of a sub-system. Previous work has identified serious objections to such an interpretation because it apparently leads to macroscopic superpositions and physically unacceptable instabilities near degeneracies. We show that both these problems are solved if the sub-system consists of a large number of coarse grained degrees of freedom as one expects in order to make contact with the classical world. We further argue that coarse graining is a necessary ingredient because measuring devices have both finite spatial and temporal resolutions. What results is an interpretation in which both decoherence and coarse graining play key roles and from which the rules of the Copenhagen interpretation are seen to emerge in realistic situations that include the measurement of the position of a particle and a decay process.

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arXiv2013

Overview of large N QCD with chemical potential at weak and strong coupling

In this note we summarize the results from a longer article on obtaining the QCD phase diagram as a function of the temperature and chemical potential at large Nc and large Nf in the weak and the strong coupling limits. The weak coupling phase diagram is obtained from the Polyakov line order parameter, and the quark number, calculated using 1-loop perturbation theory for QCD formulated on S^1 x S^3. The strong coupling phase diagram is obtained from the same observables calculated at leading order in the lattice strong coupling and hopping parameter expansions. We show that the matrix models in these two limits agree at temperatures and chemical potentials which are not too high, such that observables in the strongly-coupled theory can be obtained from the observables in the weakly-coupled theory, and vice versa, using a simple transformation of variables.

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