The research-level tag applies to questions that arise in graduate and post-secondary work. These questions often require domain-specific knowledge and could not be answered from a general source or may be beyond the level typically covered by Wikipedia and other popular sources. research-level ...

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0answers
174 views

The Integral Trick and An Equality in Nakajima's Lecture

In Nekrasov et al's series papers MNS, they calculate such kinds of integral $$ \frac{E_1 E_2}{N(2\pi i)^N(E_1+E_2) }\oint d\phi_1 \wedge d\phi_2\wedge \ldots\wedge d\phi_N \prod_{i<N} (-\phi_i) \...
7
votes
0answers
224 views

Electric potential of a spheroidal gaussian

I'm looking for results that compute the electrostatic potential due to a spheroidal gaussian distribution. Specifically, I'm looking for solutions of equations of the form $$ \nabla^2\Phi=N\exp\left({...
7
votes
0answers
355 views

Information geometry of 1D Ising model in complex magnetic field regime

Consider the one-dimensional Ising model with constant magnetic field and node-dependent interaction on a finite lattice, given by $$H(\sigma) = -\sum_{i = 1}^N J_i\sigma_i\sigma_{i + 1} - h\sum_{i = ...
7
votes
0answers
138 views

What is the state-of-the-art on spacelike singularities in string theory?

What lessons do we have from string theory regarding the fate of singularities in general relativity? What happens to black hole singularities? What happens to cosmological singularities? Which ...
7
votes
0answers
94 views

Do bipartite spin glasses have simple relaxation dynamics?

From what I gather, a Boltzmann machine (BM) is essentially a spin glass with no applied field evolving under Glauber dynamics (if this is at all mistaken, I don't think it will be off enough to ...
6
votes
1answer
94 views

Are there stable string theory vacua with non-minimal cosmological constant?

Naive reasoning suggests that a string theory vacuum with cosmological constant Lambda1 is always unstable as long as there is a string theory vacuum with cosmological constant Lambda2 < Lambda1 ...
6
votes
3answers
547 views

Whis is the difference between charge fractionalization in 1D and 2D?

Both 1D Polyacetelene and 2D fractional quantum Hall state can support fractional excitations. But as I can see, there are some differences: the ground state of Polyacetelene breaks translational ...
6
votes
2answers
1k views

Definition of short range entanglement

When studying Symmetry Protected Topological phases, one needs to define what a short range entangled (SRE) states means. But there appears to be different definitions that are not equivalent to each ...
6
votes
1answer
120 views

Allowed states vis-a-vis allowed dynamics in generalized probabilistic theories (GPTs)

In his work on information processing in GPTs http://arxiv.org/abs/quant-ph/0508211 Barrett speculates that the trade-off between allowed states and the allowed dynamics in a GPT is optimal in quantum ...
6
votes
2answers
257 views

fitting free QFTs into the Haag-Kastler algebraic formulation

Has the free Klein-Gordon quantum field theory been fitted into the Haag-Kastler algebraic framework? (Actually, John Baez told me "yes", and he should know.) If so, can you describe the basic ...
6
votes
1answer
331 views

Status of the little hierarchy problem

What is the current thinking on the little hierarchy problem in light of a potential Higgs mass above 120 GeV? A few years ago, at least, I remember various phenomenologists saying that this at least ...
6
votes
1answer
187 views

Quantum mechanics as a Markov process

I am currently involved in some understanding on this matter with a colleague of mine. I know all the literature about but I do not know the state of art. Please, could you provide some relevant ...
6
votes
2answers
356 views

Seiberg-Witten theory and Superconductivity

There seems to have some (deep) relation between Seiberg-Witten theory and superconductivity. e.g. this Witten paper. Q: Could someone introduce the relations between the twos both physically in ...
6
votes
2answers
614 views

Branch-point twist fields and operator insertions on a Riemann manifold

I am having trouble understanding how Eq (2.6) in this paper (PDF) $$Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}$$ generalizes to ...
6
votes
3answers
397 views

Modular invariance for higher genus

As far as I understand, there are roughly 2 "common" kinds of 2D conformal field theories: Theories that are defined only on the plane, more precisely, on any surface of vanishing genus. Such a ...
6
votes
1answer
153 views

Optimality of the CHSH strategy

The maximum achievable probability of the Clauser-Horne-Shimony-Holt game is $\cos^2(\pi/8)\approx85.355\%,$ which can be proved with Tsirelson's inequality. But I don't imagine that this remained ...
6
votes
2answers
171 views

Infinity of running couplings

A Landau pole - an infinity occurring in the running of coupling constants in QFT is a known phenomena. How does the Landau pole energy scale behave if we increase the order of our calculation, (more ...
6
votes
1answer
300 views

Two-loop regularization

Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral $$ I(p)=\int\frac{d^4p_1}{(2\pi)^4}\frac{d^4p_2}{(2\pi)^4}\frac{1}{(p_1^2+m_1^2)(...
6
votes
1answer
410 views

Scherk-Schwarz and other compactifications?

I have been thinking about various types of compactifications and have been wondering if I have been understanding them, and how they all fit together, correctly. From my understanding, if we want ...
6
votes
2answers
764 views

Feynman rules with helicity states.

Whenever Feynman rules are stated they are always without any mention of the helicities - this I find to be very confusing. How does one introduce and account for that? Is there an intuitive/simple ...
6
votes
1answer
151 views

States diagonal in the tensor product of Bell states.

Bell-diagonal states are 2-qubit states that are diagonal in the Bell basis. Since those states lie in $\mathbb{C}^{2} \otimes \mathbb{C}^{2}$, the Peres-Horodecki criterion is a sufficient condition ...
6
votes
1answer
313 views

Uniqueness of the 5 string theories

This question combines several sub-questions, the common theme being: why the known 5 string theories are unique? Firstly, regarding heterotic theory. I understand the only allowed gauge groups are $...
6
votes
1answer
149 views

Poisson structure on moduli space of CFTs

The moduli space of CFTs with central charge 26 forms the classical phase space of bosonic string theory, in some sense. Similarily the moduli space of SCFTs with central charge 10 forms the classical ...
6
votes
1answer
228 views

What is known about Higgs LHC machine learning algorithm for identifying Higgs events?

Recently many LHC-affiliated organizations and otherwise announced the Higgs ML learning challenge (in May) running over the summer. There are many competing teams and significant results posted ...
6
votes
1answer
256 views

Proof that we can always find a gauge transformation such that $A_0=0$?

I'm trying to follow Coleman's proof from his lectures "Aspects of Symmetry" on page 200-201. He proofs it is always possible to work in the temporal gauge for a general Yang-Mills-Higgs theory. I ...
6
votes
1answer
202 views

Background Gauge Condition In Moduli Space

I'm really confused on the background gauge condition for the moduli space of BPS-monopoles: \begin{equation} D_i \delta A_i + e [\phi , \delta \phi]=0 \end{equation} I can see that this conditions ...
6
votes
1answer
55 views

Which arguments for $m_u \approx 0$ are still in the market?

The RPP note on quarks masses has traditionally carried, and it is still there, the comment that It is particularly important to determine the quark mass ratio mu/md, since there is no strong CP ...
6
votes
1answer
397 views

Some questions about the BCFW reduction

I am trying to give a fast sketch of what the BCFW reduction does and embed within it some questions at the steps which I don't seem to understand clearly. The first bullet point is sort of a very ...
6
votes
2answers
320 views

can gapped systems have gravitational anomalies?

The question is in the title. If it is possible, what are some examples of gapped systems--either quantum field theories or condensed matter systems--which exhibit some kind of anomaly when coupled ...
6
votes
1answer
119 views

Semileptonic decays of the $B_c$ meson

I am struggling with calculating the exclusive semileptonic $B_c^+\rightarrow J/\psi l^+\nu_l$ decay. I learnt that the amplitude is given by a product of the leptonic current $L^{\mu}$ and the ...
6
votes
1answer
199 views

Spin-ice materials with strong quantum fluctuations

Spin-ice materials are insulating materials where spins form a 3D pyrochlore lattice and have a frustrated magnetic interaction. The spin dynamics in most spin-ice materials is very classical and has ...
6
votes
1answer
133 views

$\pm$ (light-cone?) notation in supersymmetry

I would like to know what is exactly meant when one writes $\theta^{\pm}, \bar{\theta}^\pm, Q_{\pm},\bar{Q}_{\pm},D_{\pm},\bar{D}_{\pm}$. {..I typically encounter this notation in literature on $2+...
6
votes
1answer
135 views

How does a geodesic equation on an n-manifold deal with singularities?

My general premise is that I want to investigate the transformations between two distinct sets of vertices on n-dimensional manifolds and then find applications to theoretical physics by: ...
6
votes
1answer
174 views

random matrix ensembles from BMN model

My friends working on Thermalization of Black Holes explained solutions to their matrix-valued differential equations (from numerical implementation of the Berenstein-Maldacena-Nastase matrix model) ...
6
votes
1answer
926 views

Definition and difference between the R-symmetry and the $U(1)_R$ internal symmetry

For a general ${\cal N}$ the R-symmetry group is $U({\cal N})$ but for the ${\cal N}=2$ case why is it $SU(2)$ ? I guess it is again different for ${\cal N}=4$. How does one understand this? One ...
6
votes
3answers
2k views

What causes a Phase-Transition?

A phase transition occurs when for example, heat is applied continuously to a liquid and after a certain time it converts into a gas. How does this process work in detail? Is their a chain reaction ...
6
votes
1answer
384 views

partial trace with sparse matrices

Let $\rho_{ABCD}$ be a sparse matrix of 4 systems each in a $d$-dimensional Hilbert space. For $d<7$ in a reasonable time (few seconds) I able to perform the partial trace $\rho_{AD}$ using the ...
6
votes
1answer
548 views

About the definition/motivation/properties of the twisted chiral superfield in ${\cal N}=2$ theories in $1+1$ dimensions

The following is in the context of the ${\cal N}=2$ supersymmetry in $1+1$ dimensions - which is probably generically constructed as a reduction from the ${\cal N}=1$ case in $3+1$ dimensions. In ...
6
votes
1answer
575 views

Defining the ground state energy of a QFT

I would like to hear of some general discussion on how is the ground state and its energy defined in QFT and how does one go about finding it. (..at least in some simple cases I have seen the use of ...
6
votes
1answer
204 views

Asymptotic Completeness, generalized free fields, and the relationship of thermodynamics with infinity

Asymptotic completeness is a strong constraint on quantum field theories that rules out generalized free fields, which otherwise satisfy the Wightman axioms. If we were to take a limit of a list of ...
6
votes
1answer
255 views

Parametrisation of general MSSM/SUSY based on collider experiment observables

The full MSSM contains 120 parameters. In SUSY searches, one usually picks a model like MSUGRA which makes a few assumptions and only has 5 free parameters like $m_0$, $m_{1/2}$, .... Now, I'm ...
6
votes
0answers
178 views

Obtaining the canonical distribution from Fokker-Planck equation?

First I will provide a summary of the problem. Subsequently, I will provide more detail regarding the problem. Please note that entropy is in units of the Boltzmann constant. Summary I have a Fokker-...
6
votes
0answers
376 views

Strong interacting v.s. Strong Coupling v.s. Strong Correlated

One of the active research areas in present is Strong interacting, Strong Coupling, Strong Correlated regime of the phases of matters. It seems to me that some physicists in the fields often mix the ...
6
votes
0answers
230 views

Could sphaleron-induced proton decay also cause vacuum decay?

I will say right away that I don't mean standard-model sphalerons, I mean the sphalerons of some extension of the standard model. The reason to even think about this is last year's paper by Frampton ...
6
votes
0answers
164 views

Looking for modern results in semiclassical physics and relevant references

What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the semiclassical regime? To be clear, I'm not ...
6
votes
0answers
190 views

Toda equations and surface operator

I would like to know the reason why the equation (14) in the paper by Yamada is called the Toda equation. \begin{equation} \left[\frac12\sum_{i=1}^N\left(y_i\frac{\partial}{\partial y_i}-y_{i+1}\frac{\...
6
votes
0answers
304 views

Partition Functions in (A)dS/CFT

I'm trying to understand some aspects of dS/CFT, and I'm running into a little trouble. Any help would be much appreciated. In arXix:1104.2621, Harlow and Stanford showed that the late-time Hartle-...
6
votes
0answers
39 views

Classic mass predictions from Left-Right models with discrete symmetries?

I am covering the classic literature on predictions of Cabibbo angle or other relationships in the mass matrix. As you may remember, this research was a rage in the late seventies, after noticing that ...
6
votes
0answers
113 views

String landscape in different dimensions

For D = 11 large (uncompactified) spacetime dimensions, the only "string theory" vacuum is M-theory For D = 10, there are 5 vacua. Or maybe it's more correct to say 4, since type I is S-dual to $Spin(...
6
votes
0answers
65 views

Status of large-scale structure formation within cosmology today

Since the CMB results of the past decade, would it be fair to say that the consensus among cosmologists is that cosmic strings are no longer considered as a (major) source for density perturbations? ...