The Quotient of a Category by the Action of a Monoidal Category

We introduce the notion of the quotient of a category $C$ by the action $A : M \longrightarrow C \times C$ of a unital symmetric monoidal category $M$. The quotient $C/M$ is a 2-category. We prove its existence and uniqueness by first showing that every small 2-category has a presentation in terms of generators and relations and then describing the generators and relations needed for the quotient $C/M$

The Geometry of The Entropic Principle and the Shape of the Universe

Ooguri, Vafa, and Verlinde have outlined an approach to two-dimensional accelerating string cosmology which is based on topological string theory, the ultimate objective being to develop a string-theoretic understanding of "creating the Universe from nothing". The key technical idea here is to assign *two different* Lorentzian spacetimes to a certain Euclidean space. Here we give a simple framework which allows this to be done in a systematic way. This framework allows us to extend the construction to higher dimensions. We find then that the general shape of the spatial sections of the newly created Universe is constrained by the OVV formalism: the sections have to be flat and compact.Comment: 24 pages, 4 eps figures, improved exposition of Euclidean/Lorentzian smoothin

Lorentz Violation in Fermion-Antifermion Decays of Spinless Particles

If Lorentz and CPT violation exist, they could affect the decays of scalar and pseudoscalar particles. For a decay into a fermion and an antifermion (not necessarily of the same mass), both the total decay rate and the outgoing particle distribution may be modified, through interference between the conventional decay mechanism and a separate Lorentz-violating mechanism. The modifications are sensitive to forms of Lorentz violation that are otherwise rather difficult to study, since at tree level they do not affect particle propagation, but only interaction vertices. Using existing experimental data on charged pion decay, it is possible to constrain three parameters in the modified pion-muon-neutrino coupling at better than the $10^{-9}$ level; these are the first bounds on these quantities.Comment: 16 page

A Holographic Bound on Cosmic Magnetic Fields

Magnetic fields large enough to be observable are ubiquitous in astrophysics, even at extremely large length scales. This has led to the suggestion that such fields are seeded at very early (inflationary) times, and subsequently amplified by various processes involving, for example, dynamo effects. Many such mechanisms give rise to extremely large magnetic fields at the end of inflationary reheating, and therefore also during the quark-gluon plasma epoch of the early universe. Such plasmas have a well-known holographic description in terms of a thermal asymptotically AdS black hole. We show that holography imposes an upper bound on the intensity of magnetic fields ($\approx \; 3.6 \times 10^{18}\;\; \text{gauss}$ at the hadronization temperature) in these circumstances; this is above, but not far above, the values expected in some models of cosmic magnetogenesis.Comment: 16 pages, 2 figures, explicit numerical value given for the bound, improved discussion of implications for superadiabatic amplification, version to appear in Nucl Phys

Angular Momentum in QGP Holography

The quark chemical potential is one of the fundamental parameters describing the Quark-Gluon Plasma produced by sufficiently energetic heavy-ion collisions. It is not large at the extremely high temperatures probed by the LHC, but it plays a key role in discussions of the beam energy scan programmes at the RHIC and other facilities. On the other hand, collisions at such energies typically (that is, in peripheral collisions) give rise to very high values of the angular momentum density. Here we explain that holographic estimates of the quark chemical potential of a rotating sample of plasma can be very considerably improved by taking the angular momentum into account.Comment: 22 pages, 2 figures, version to appear in Nuclear Physics

Certainty, Probability, and Stalin’s Great Party Purge

In 1935, Stalin decided to purge his own party to consolidate power in the Soviet government. Since the inception of historical research about this event, a debate has developed regarding the number of arrests and deaths of Soviets ordered by Stalin. This study will examine the figures calculated by Western historians to determine where correlation and discrepancy exist. The importance of this research is to assess the reasons why such dramatic statistical differences exist among various historians. The historians’ sources show the difficulty of determining accurate figures because of the secretive nature of the Soviet government and only partial opening of Soviet archives

ADVANCING THE SEPARATION SCIENCES THROUGH THE DELIVERY OF NEW MATERIALS, TECHNOLOGY AND METHODOLOGY.

A thesis and collection of works submitted to Plymouth University in partial fulfilment for the degree of DOCTOR OF SCIENC

How Does the Quark-Gluon Plasma Know the Collision Energy?

Heavy ion collisions at the LHC facility generate a Quark-Gluon Plasma (QGP) which, for central collisions, has a higher energy density and temperature than the plasma generated in central collisions at the RHIC. But sufficiently peripheral LHC collisions give rise to plasmas which have the \emph{same} energy density and temperature as the "central" RHIC plasmas. One might assume that the two versions of the QGP would have very similar properties (for example, with regard to jet quenching), but recent investigations have suggested that \emph{they do not}: the plasma "knows" that the overall collision energy is different in the two cases. We argue, using a gauge-gravity analysis, that the strong magnetic fields arising in one case (peripheral collisions), but not the other, may be relevant here. If the residual magnetic field in peripheral LHC plasmas is of the order of at least $eB\,\approx \,5\,m^2_{\pi}$, then the model predicts modifications of the relevant quenching parameter which approach those recently reported.Comment: 16 pages, one figure; version to appear in Nuclear Physics

There is No Ambiguity in the Radiatively Induced Gravitational Chern-Simons Term

Quantum corrections to Lorentz- and CPT-violating QED in flat spacetime produce unusual radiative corrections, which can be finite but of undetermined magnitude. The corresponding radiative corrections in a gravitational theory are even stranger, since the term in the fermion action involving a preferred axial vector $b^{\mu}$ would give rise to a gravitational Chern-Simons term that is proportional $b^{\mu}$, yet which actually does not break Lorentz invariance. Initially, the coefficient of this gravitational Chern-Simons term appears to have the same ambiguity as the coefficient for the analogous term in QED. However, this puzzle is resolved by the fact that the gravitational theory has more stringent gauge invariance requirements. Lorentz symmetry in a metric theory of gravity can only be broken spontaneously, and when the vector $b^{\mu}$ arises from spontaneous symmetry breaking, these specific radiative corrections are no longer ambiguous but instead must vanish identically.Comment: 16 page