Questions tagged [research-level]

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 questions should not require new or groundbreaking research and results to answer.

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2answers
549 views

Gauge invariance for electromagnetic potential observables in test function form

This is a reference request for a relationship in quantum field theory between the electromagnetic potential and the electromagnetic field when they are presented in test function form. $U(1)$ gauge ...
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1answer
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Principle behind fidelity balance in quantum cloning

If we do optimal state estimation on an unknown qubit, we can recreate a state with fidelity $F_c=2/3$ with respect to the original. Let us define the "quantum information content" $I_q=1-2/3=1/3$ as ...
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3answers
434 views

POVMs that do not require enlargement of the Hilbert space

The usual justification for regarding POVMs as fundamental measurements is via Neumark's theorem, i.e., by showing that they can always be realized by a projective measurement in a larger Hilbert ...
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2answers
382 views

Discussions of the axioms of AQFT

The most recent discussion of what axioms one might drop from the Wightman axioms to allow the construction of realistic models that I'm aware of is Streater, Rep. Prog. Phys. 1975 38 771-846, "...
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1answer
224 views

How can one build a multi-scale physics model of fluid flow phenomena?

I am working on a problem in Computational Fluid Dynamics, modeling multi-phase fluid flow through porous media. Though there are continuum equations to describe macroscopic flow (darcy's law, ...
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2answers
124 views

Examples of heterotic CFTs

I'm trying to get a global idea of the world of conformal field theories. Many authors restrict attention to CFTs where the algebras of left and right movers agree. I'd like to increase my intuition ...
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1answer
179 views

How many times do solar protons repeatedly fuse and fission before they form deuteron

In the proton-proton chain reaction in the Sun, the first step is $$p + p \rightarrow \; ^2_2{\rm He} .$$ After this, the most likely thing to happen next is that the reverse reaction occurs: the $^...
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1answer
127 views

Higgs Field - Is its discovery truly “around the corner”?

Rather surprised I haven't seen many questions or discussion regarding the rumored confirmation of the Higgs field. As I understand it, the energies where they saw things were actually quite a bit ...
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1answer
421 views

Characters of $\widehat{\mathfrak{su}}(2)_k$ and WZW coset construction

I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine ...
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1answer
1k views

Reduced density matrices for free fermions are thermal

Many recent papers study entanglement in eigenstates of fermionic free hamiltonians (normally on a lattice) using the basic assumption that the reduced density matrices are thermal (e.g. Peschel 2003)....
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1answer
161 views

Metric interpretation of self-adjoint extensions?

I am wondering if beyond physical interpretation, the one dimensional contact interactions (self-adjoint extensions of the the free Hamiltonian when defined everywhere except at the origin) have a ...
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1answer
287 views

Some questions on a version of the O'Raifeartaigh model

This form is taken from a talk by Seiberg to which I was listening to, Take the Kahler potential ($K$) and the supersymmetric potential ($W$) as, $K = \vert X\vert ^2 + \vert \phi _1 \vert ^2 + \...
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1answer
467 views

The difference between $\mathcal{N}=2$ short multiplets and BPS states

I have some questions about the construction of $\mathcal{N}=2$ supermultiplets for chiral matter. I know that the supermultiplet should not include spin one states since they are always in the ...
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486 views

Capturing (perturbatively) non-equilibrium field theory effects using “elementary” methods

I am considering a system of two interacting scalar fields: $\psi$, and $\phi$. The Lagrangian is given by: \begin{equation} \mathcal{L}[\psi]=\frac{1}{2}\partial_\mu\psi\partial^\mu\psi+\frac{1}{2}\...
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1answer
714 views

How to prove quantum N=4 Super-Yang-Mills is superconformal?

I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations Also, does a non-perturbative proof exist?
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792 views

What is the physical difference between states and unital completely positive maps?

Mathematically, completely positive maps on C*-algebras generalize positive linear functionals in that every positive linear functional on a C*-algebra $A$ is a completely positive map of $A$ into $\...
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1answer
2k views

AGT conjecture and WZW model

In 2009 Alday, Gaiotto and Tachikawa conjectured an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov ...
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3answers
824 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 ...
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2answers
734 views

Wilson Loops as raising operators

Consider a U(1) Chern Simons theory on a torus $\mathbb{T}$: \begin{align} L &= \frac{k}{4\pi} \int_{\mathbb{T}} a \partial a \end{align} where a is some U(1) gauge field, $k\in\mathbb{Z}$ and we ...
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1answer
137 views

Renyi fractal dimension $D_q$ for non-trivial $q$

For a probability distribution $P$, Renyi fractal dimension is defined as $$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$ where $R_q$ is Renyi entropy of order $q$ ...
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1answer
361 views

Do thermodynamic quantities in CFT correspond to something different in AdS/CFT?

From what I've (hopefully) understood from the AdS/CFT correspondence, physical quantities have a dual version. For example, the position in the bulk is the scale size (in renormalization), and waves ...
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1answer
358 views

Global symmetry in string theory

It is often stated that in quantum gravity only charges coupled to gauge fields can be conserved. This is because of the no hair theorem. If a charge is coupled to a gauge field then when it falls ...
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1answer
838 views

On a rigorous definition of Feynman's functional integral$.$

It is often stated that there is no mathematically rigorous definition of Feynman's functional integral, except for some very specific examples. I may be very naïve, but to me there is at least one ...
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2answers
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Realization of Witten-type topological quantum field theory in condensed matter physics

It is well-known that some exotic phases in condensed matter physics are described by Schwarz-type TQFTs, such as Chern-Simons theory of quantum Hall states. My question is whether there are condensed ...
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1answer
286 views

Quantum gravity at D = 3

Quantization of gravity (general relativity) seems to be impossible for spacetime dimension D >= 4. Instead, quantum gravity is described by string theory which is something more than quantization (...
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1answer
227 views

Superconformal Multiplet Calculus in 6D

A convenient method for dealing with off-shell formulations of supergravity theories is provided by the superconformal multiplet calculus. This calculus was originally constructed for 4d ${\cal N}=2$ ...
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1answer
107 views

N=2 SSM without a Higgs

In arXiv:1012.5099, section III, the authors describe a supersymmetric extension to the standard model in which there is no Higgs sector at all, in the conventional sense. The up-type Higgs is a ...
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1answer
143 views

Matrix geometry for F-strings

A stack of N D-branes has the strange property that the traverse D-brane coordinates are matrix-valued. When the matrices commute, they can be interpreted as ordinary coordinates for N ...
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1answer
529 views

Quantum mechanical gravitational bound states

The quantum mechanics of Coloumb-force bound states of atomic nuclei and electrons lead to the extremely rich theory of molecules. In particular, I think the richness of the theory is related to the ...
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2answers
687 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 ...
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1answer
2k views

Kramers-Kronig relations for the electron Self-Energy Σ

I'm currently studying an article by Maslov, in particular the first section about higher corrections to Fermi-liquid behavior of interacting electron systems. Unfortunately, I've hit a snag when ...
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1answer
704 views

precise definition of “moduli space”

I'm curious what the precise definition of the moduli space of a QFT is. One often talks about the classical moduli space, which then can get quantum corrections. Does this mean the quantum moduli ...
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1answer
651 views

False vacuum in axiomatic QFT

There is an elegant way to define the concept of an unstable particle in axiomatic QFT (let's use the Haag-Kastler axioms for definiteness), namely as complex poles in scattering amplitudes. Stable ...
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0answers
98 views

status of +4/3 scalar as explanation of $t\bar t$ asymmetry

One of the early proposals for the Tevatron asymmetry on $t \bar t$ was a "fundamental diquark" with a charge (and hypercharge) +4/3, either in a triplet or a sextet colour. I am interested on the ...
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3answers
196 views

Depolarizing threshold for CSS codes

Many years ago, when CSS codes were first invented, the error threshold of p=0.11 was found when bit and phase flips are independent. Has a threshold yet been found for the case of depolarizing noise?
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4answers
1k views

Different kinds of S-matrices?

It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...
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2answers
1k views

Is there a published upper limit on the electron's electric quadrupole moment?

I understand an electric quadrupole moment is forbidden in the standard electron theory. In this paper considering general relativistic corrections (Kerr-Newman metric around the electron), however, ...
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3answers
2k views

Group Cohomology and Topological Field Theories

I have a two-part question: First and foremost: I have been going through the paper by Dijkgraaf and Witten "Group Cohomology and Topological Field Theories". Here they give a general definition for ...
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2answers
9k views

Some Korean researchers saying that they solved Yang-Mills existence and mass gap problem

Today, Korean media is reporting that a team of South Korean researchers solved Yang-Mill existence and mass gap problem. Did anyone outside Korea even notice this? I was not able to notice anything ...
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1answer
259 views

What compactifications of the Poincaré group have been studied?

As we know, the Poincaré group is non-compact. Poincaré invariance has been observed at velocities and energies up to $10^{20}$ eV in cosmic rays. The other day, I was thinking about how the $SU(2)$ ...
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1answer
302 views

What evidence do we have for S-duality in N=4 Super-Yang-Mills?

Do we have anything resembling a proof*? Or is it just a collection of "coincidences"? Also, do we have evidence from lattice gauge theory computations? *Of course I'm not talking about a proof in ...
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1answer
815 views

What is the significance of the branch cut in renormalization group logarithms?

What is the physical significance of the branch cut in renormalization group logarithms? (Is this just an avatar of the optical theorem, or is there something to be understood about these logarithms ...
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1answer
245 views

Why isn't there heterotic holographic QCD?

I think the question speaks for itself... Top-down holographic QCD, like Sakai-Sugimoto, always involves the Type II string. There are one or two papers on hQCD using the Type 0 string. But I can't ...
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1answer
228 views

About the stability of the ground state of the bosonic string

In Polchinski's string theory vol 1, p. 23, it is said "It is a complicated question whether the bosonic string has any stable vacuum, and the answer is not known." The book was published on 1998. ...
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1answer
195 views

Conformal QFTs for $D > 2$

Which conformal QFTs do we know for spacetime dimension $D > 2$? I know that for $D = 4$ we have ${\cal N} = 4$ SYM and some ${\cal N} = 2$ supersymmetric Yang-Mills + matter models. What is ...
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2answers
603 views

Why aren't the spin-3/2 fields in the (3/2,0)+(0,3/2) representation?

Why is it that spin-$\frac 32$ fields are usually described to be in the $(\frac 12, \frac 12)\otimes[(\frac 12,0)\oplus(0,\frac 12)]$ representation (Rarita-Schwinger) rather than the $(\frac 32,0)\...
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2answers
322 views

Torsion and gauge invariant EM kinetic term

Everytime I hear about adding torsion to GR, something struggles me: how do you create a kinetic term for the electromagnetic field that is still gauge-invariant? One of the consequences of torsion is ...
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1answer
91 views

Dual Pairs in Four Dimensions

Following the conversation here, I am wondering if anyone knows of an example of dual pair with 4-dimensional N=1 SUSY which relates a non-Abelian gauge theory on one side to a theory with a ...
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1answer
270 views

Boundary currents for Asymptotic Symmetry Group (ASG)

In the context of asymptotic symmetry groups, what is a boundary current? Why is it called a "current"? Context: I'm reading Strominger's recent paper on Asymptotic symmetry group of Yang-Mills (...
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1answer
282 views

How does one geometrically quantize the Bloch equations?

I've just now rated David Bar Moshe's post (below) as an "answer", for which appreciation and thanks are given. Nonetheless there's more to be said, and in hopes of stimulating further posts, I've ...

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