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3
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1answer
45 views

Can one make a synthetic dimension “curl around” into a cylinder?

A really cool recent proposal, Synthetic Gauge Fields in Synthetic Dimensions. A. Celi et al. Phys. Rev. Lett. 112, 043001 (2014), arXiv:1307.8349, shows how you can simulate a synthetic ...
3
votes
1answer
63 views

What are the latest findings on the topology and size of the universe?

The paper G. Aslanyan & A.V. Manohar, The Topology and Size of the Universe from the Cosmic Microwave Background, JCAP 06 (2012) 003, arXiv:1104.0015, uses the 7-year WMAP data. Has any ...
3
votes
1answer
134 views

Moving the endpoints of a wormhole towards each other

Suppose we have a perfectly safe portal/wormhole and we place the two endpoints facing each other so that a person between them would see an endless corridor (with infinite number of herself). What ...
2
votes
1answer
134 views

$U(1)$ 5-dimensional Kaluza-Klein topological defects

Five-dimensional Kaluza-Klein theory is well-known to predict that the electromagnetic field can be described as a curled additional dimension over four-dimensional spacetime. That is, you only need ...
12
votes
0answers
366 views

Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An ...
10
votes
0answers
325 views

p-Adic String Theory and the String-orientation of Topological Modular Forms (tmf)

I am going to ask a question, at the end below, on whether anyone has tried to make more explicit what should be a close relation between p-adic string theory and the refinement of the superstring ...
9
votes
0answers
165 views

Making new sense of the three-body problem in the light of Maryam Mirzakhani math contributions

I am unfamiliar with moduli spaces and ergodic theory which appear to be essential in Maryam Mirzakhani's math contributions which won her the Fields Medal. However, I am well conversant in essential ...
6
votes
0answers
45 views

What is the importance of studying degeneration on $M_g$

Let $M_g$ be the moduli space of smooth curves of genus $g$. Let $\overline{M_g}$ be its compactification; the moduli space of stable curves of genus $g$. It seems to be important in physics to study ...
5
votes
0answers
127 views

Why can apparent horizon be computed based on its local geometry?

Why can apparent horizon be computed based on its local geometry? In the paper titled Black Holes, Geometric Flows, and the Penrose Inequality in General Relativity by Hubert L. Bray, has been ...
4
votes
0answers
44 views

Solutions of nonlinear systems invariant wrt. perturbations (looking for applications)

I want to ask if the following purely mathematical problem (that I'm working on) might have some applications to physics. The problem in a nutshell: describe properties of solution sets of real ...
4
votes
0answers
271 views

Squashed 3-sphere?

What is a squashed 3-sphere? In context of quantum gravity. I stumbled upon a term 'squashed 7 sphere' but that's concerning supersymmetry. Is it just normal 3-sphere metric, that is just 'squashed' ...
4
votes
0answers
110 views

Some questions about spacetime topology, causality structures and other GR businesses

1) What are the exact conditions required for the canonical transformation? Most papers just assume away with global hyperbolicity, but is there a more general condition for it? "Quantum gravity in ...
4
votes
0answers
118 views

Alternate geodesic completions of a Schwarzschild black hole

The Kruskal-Szekeres solution extends the exterior Schwarzschild solution maximally, so that every geodesic not contacting a curvature singularity can be extended arbitrarily far in either direction. ...
3
votes
0answers
56 views

Branes wrapping curves in M-theory. What does it mean?

What does it mean that a M5-branes wraps a holomorphic curve in M-theory? In specific a lot of Vafa's paper involve various branes (not only M5) wrapping some cycles. What does this really mean ...
3
votes
0answers
67 views

Asymtotically flat spacetime applicable for spacetimes which are not diffeomorphic to $\mathbb{R}^4$

I wanted to investigate changes on a compact 4-manifold $M$. More specifically it is the K3-surface. I follow a paper by Asselmeyer-Maluga from 2012. The idea there was to make sure that the manifold ...
3
votes
0answers
58 views

Physical consequences of non-trivial quantum states homology

The set of quantum states of a finite dimensional system is a complex projective space, whose homology groups are non-trivial http://en.wikipedia.org/wiki/Complex_projective_space#Homology. Has this ...
3
votes
0answers
83 views

1+1D Bosonization on a line segment or a compact ring

I have been informed that 1+1D Bosonization/Fermionization on a line segment or 1+1D Bosonization/Fermionization a compact ring are different - Although I know that Bosonization can rewrite fermions ...
3
votes
0answers
56 views

How many unequivalent Seifert surfaces appear in a AdS/CFT extension?

When introducing the 't Hooft diagrams from Feynman diagrams on a torus has there been a classification in terms of knots and Seifert surfaces?
3
votes
0answers
267 views

Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?

A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
3
votes
0answers
97 views

are pinch-off bubbles valid solutions to general relativity?

are bubbles of spacetime pinching-off allowed solutions to general relativity? With "pinch-off bubble" i really mean a finite 3D volume of space whose 2D boundary decreases until it reaches zero and ...
3
votes
0answers
226 views

What are the topics of string theory that are comprehensible with only a mathematical background on Manifolds and Algebraic Topology?

What are the topics of string theory that are comprehensible with only a mathematical background on manifolds and algebraic topology? Also, I have read only the first four chapters in Peskin & ...
2
votes
0answers
70 views

Axion strings and spontaneously broken symmetry

I have two question about axion strings: Why their appearance is connected with spontaneously broken symmetry? How to demonstrate that? Why they are stable topological configurations (look to the ...
2
votes
0answers
28 views

When can a $k$-cycle wrap around a manifold?

According to the paper ``Heterotic and Type I String Dynamics from Eleven Dimensions'' (page 7): Even when the topology is wrong -- for instance on $\mathbb{R}^{11}$ where there is no two-cycle ...
2
votes
0answers
56 views

Validity of topological thermodynamics?

I've been reading some material by R. Kiehn, developing a topological approach to non-equilibrium thermodynamics through Cartan forms, where the fundamental claim is that irreversible processes are ...
2
votes
0answers
89 views

How to calculate topological charge?

For a complex vector field in two dimensions with one or more phase singularity - a point where the field amplitude is zero and the phase is undefined - how do you explicitly calculate the total ...
2
votes
0answers
83 views

What is elliptic genera?

What is elliptic genera in physics? Reading many relevant papers, they just defined elliptic genus as sort of partition function. I try to find useful materials to explain it, but I couldn't find ...
2
votes
0answers
74 views

If $S$ is a closed achronal set in a spacetime, any timelike curve starting at a point in $I^+[S]$ and ending at a point in $I^-[S]$ interset $S$?

Suppose $S$ is an achronal set in a spacetime $M$. And $S$ is closed. At the same time, any null geodesic of $M$ intersects $S$. Then, why does any timelike curve from $I^+[S]$ to $I^-[S]$ intersect ...
2
votes
0answers
105 views

Interesting Hamiltonian System

The definition of a Hamiltonian system I am working with is a triple $(X,\omega, H)$ where $(X,\omega)$ is a symplectic manifold and $H\in C^\infty(X)$ is the Hamiltonian function. I am wondering if ...
2
votes
0answers
97 views

Some questions on the Wilson loop in the projective construction?

Based on the previous question and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij}'\psi_j+H.c.)$, we ...
1
vote
0answers
29 views

Global cosmic strings evolution

Recently I've read about axion string. It can be shown that the energy per unit length of the string located along $z$ axis is $$ \mu = 2 \pi f_{a}^{2}\ln\left( \frac{L}{\delta}\right), $$ where $L$ ...
1
vote
0answers
33 views
1
vote
0answers
46 views

Are topological vacua of QCD Lorentz invariant?

Are topological vacua of QCD Lorentz invariant or they mix under boosts?
1
vote
0answers
85 views

Divergence Theorem, mathematical approach to Gauss's Law?

Let $D$ be a compact region in $\mathbb{R}^3$ with a smooth boundary $S$. Assume $0 \in \text{Int}(D)$. If an electric charge of magnitude $q$ is placed at $0$, the resulting force field is ...
1
vote
0answers
170 views

Can the universe be round but still infinite?

Can the universe still be infinite in space if its curvature is > 1? Is a manifold of positive curvature necessarily compact? Does the Tarski paradox have any bearing on the finite or infinite ...
1
vote
0answers
46 views

$\mathbb{Z}_2$ topological insulators which obey inversion symmetry as well

According to Fu & Kane (2006), systems with simultaneous time-reversal invariance and inversion symmetry have their $\mathbb{Z}_2$ topological invariant given by the product of the parity ...
1
vote
0answers
85 views

Quantum phase space

Classical phase space is defined as a space in which all possible states are represented. Every state corresponds to a unique point in the phase space. On the other hand, in quantum mechanics every ...
1
vote
0answers
74 views

Euclidean AdS space in Poincaré coordinates

I have read anti-de Sitter (AdS) space and its Euclidean version both in Global and Poincaré coordinates. For Lorentzian case it is clear how one Poincaré patch cover only one half of the whole AdS ...
1
vote
0answers
45 views

Topology of a bit

From a math perspective, it seems obvious that the electric field (or voltage which ever) of a bit in a computer, when its in a stable 0, or 1 state, must have a singularity, a set of points where the ...
1
vote
0answers
86 views

Manifold for Schwarzschild and Bertotti-Robinson

In short: what is the manifold in discussion for Schwarzschild metric $$ ds^2 = -(1-\frac {2M}r)dt^2 + \frac1{1-\frac{2M}r} dr^2 + r^2 (d\theta^2 + \sin^2 \theta d\phi^2)$$ and Bertotti-Robinson ...
1
vote
0answers
38 views

Supergravity solution, metric for the total space, and connection

In supergravity solutions, one sometimes encounters the case where the manifold may be a bundle over some base space, and one has to write down the explicit metric regarding such bundle. I would like ...
1
vote
0answers
86 views

How to test that a flat metric represents a global three-torus geometry

When introducing Robertson-Walker metrics, Carroll's suggests that we consider our spacetime to be $R \times \Sigma$, where $R$ represents the time direction and $\Sigma$ is a maximally symmetric ...
1
vote
0answers
71 views

Topology of spacetime in 2+1 dimension

In the book Quantum Gravity in 2+1 dimension by S. Carlip, in the second chapter (section 2.1), he comments that a compact 3-manifold with a flat time orientable Lorentzian metric and a purely ...
1
vote
0answers
60 views

Non-locality and topology

This is a purely speculative question: Has there been any work that describes non-locality/entanglement in QM by using exotic topologies in configuration space? The 'conceptual' picture that I have ...
0
votes
0answers
28 views

How to simulate “inside-out” geometries of a structure?

How can I simulate the structural deformation of a physical material to find all possible "stable" inside out forms? For example, some dome shaped rubber caps can be pushed inside out, like the ...
0
votes
0answers
22 views

2D CFT for nontrivial topology

What is a systematic way to calculate a general $N$-points correlation function of 2D CFT for a nontrivial topology? Piece by piece of this can be found in many different CFT and String Theory ...
0
votes
0answers
42 views

Is there an analytical expression for the conductivity of the surface of topological insulators?

I have a question about the conductivity on the surface of Topological Insulators (TI): Is it accurate to model the conductivity by the Drude model (I read a paper that modeled the conductivity with ...
0
votes
0answers
69 views

Topological implications of symbolic represenation of the relativity

I have seen in the online Stanford Encyclopedia of Philosophy in the entry on Copenhagen Interpretation of Quantum Mechanics that Niels Bohr had argued that the theory of relativity is not a literal ...
0
votes
0answers
40 views

Bound states and extensive field configurations

What are extensive field configurations in QFT (instantons, monopoles etc.)? What is the difference in description of their contribution in path integral value or in $n$-point operator functions ...
0
votes
0answers
78 views

Caustic and Singularities in General Relativity

What is the relation between the formation of caustics of a family of null geodesics and the existence of an incomplete null geodesic?
0
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0answers
65 views

What is ``thermal" about a thermal quotient of EdS and EAds?

This is in continuation of my previous question and is in reference to this paper. I guess that the authors are interested in $S^n$ and $\mathbb{H}^n$ since these are the Euclideanized versions of ...