12
votes
1answer
135 views

Soliton Moduli Spaces and Homotopy Theory

The four-dimensional $SU(N)$ Yang-Mills Lagrangian is given by $$\mathcal{L}=\frac{1}{2e^2}\mathrm{Tr}F_{\mu\nu}F^{\mu\nu}$$ and gives rise to the Euclidean equations of motion $\mathcal{D}_\mu ...
4
votes
1answer
167 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 ...
1
vote
0answers
47 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
9
votes
1answer
111 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 ...
2
votes
0answers
25 views

Mirrored decoupling fermion doublers and a lattice chiral fermion / gauge theory

Nielsen Ninomiya Fermion-doubling problem has known to be a challenge to construct a chiral fermion or chiral gauge theory on the lattice. There is a proposed resolution to use so-called two mirrored ...
3
votes
0answers
65 views

Large gauge transformations for higher p-form gauge fields

Question: What is the large gauge transformations for higher p-form gauge field on a spatial d-dimensional torus $T^d$ or a generic (compact) manifold $M$? for p=1,2,3, etc or any other integers. Is ...
2
votes
1answer
58 views

Compatibility conditions of spinors and Riemannian Metrics

I came across an interesting article by Montesinos (J. Geom. Phys. 2 (1985), no. 2, 145–153.). In it, he finds that spin structures (as lifts of $SO(4)$) are not compatible with all Riemannian metrics ...
15
votes
2answers
434 views

S-Matrix in $\mathcal{N}=4$ Super-Yang Mills

This is a general question, but what is meant when people refer to the S-Matrix of $\mathcal{N}=4$ Super Yang Mills? The way I understood it is the S-Matrix is only well defined for theories with a ...
6
votes
1answer
184 views

Dirac Lagrangian density in curved spacetime

I'm trying to derive this form of the Dirac Lagrangian density in curved space-time: $$ \mathcal{L}~=~\det\left(e\right)\bar{\Psi}\Bigg ...
2
votes
0answers
37 views

Calculating the dispersion relation of dirac lagrangian in curved spacetime

I am trying to calculate the dispersion relation for a fermion in a gravitational field. So far, I have computed the equation of motion, but I am stuck trying to figure out a determinant I just can't ...
4
votes
1answer
83 views

Content of the N=2 Graviton Multiplet in 6D

I've been looking into extended Supersymmetry in higher dimensions recently. What I keep wondering about are some components of the gravity multiplet, that seem to appear from the construction of ...
3
votes
1answer
211 views

Effective action for bosonic string theory with enhanced symmetry

See these lecture http://members.ift.uam-csic.es/auranga/lect7.pdf page 17. Usually one derives the effective action from the massless states calculating amplitudes, otherwise through beta ...
11
votes
1answer
256 views

What is the CFT dual to pure gravity on AdS$_3$?

Pure $2+1$-dimensional gravity in $AdS_3$ (parametrized as $S= \int d^3 x \frac{1}{16 \pi G} \sqrt{-g} (R+\frac{2}{l^2})$) is a topological field theory closely related to Chern-Simons theory, and at ...
4
votes
3answers
321 views

Applying theorem of residues to a correlation function where the Fermi function has no poles

Let $n_F(\omega) = \large \frac{1}{e^{\beta (\omega)} + 1}$ be the Fermi function. A fermionic reservoir correlation function is given by: $$C_{12}(t) = \int_{-\infty}^{+\infty} d\omega~ ...
0
votes
1answer
188 views

Applying theorem of residues to a fermionic reservoir correlation function in order to solve the integral in the CF and obtain a summation

Applying theorem of residues to a fermionic reservoir correlation function in order to solve the integral in the correlation function and obtain a summation.
10
votes
2answers
259 views

What is the algebraic property that corresponds to a topological term?

Warning: This question will be fairly ill-posed. I have spent a lot of time trying to make it better posed without success, so please bear with me. A single $SU(2)$ spin may be represented by the ...
9
votes
1answer
226 views

Anomalies for not-on-site discrete gauge symmetries

If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
4
votes
1answer
137 views

Fermion zero modes under 1+1 D Higgs spacetime vortex?

Jackiw and Rossi had a classic paper Zero modes of the vortex-fermion system (1981). In that nice-written paper, they found fermionic zero modes of Dirac operator under nontrivial Higgs vortex in 2D ...
15
votes
1answer
616 views

Zero modes ~ zero eigenvalue modes ~ zero energy modes?

There have been several Phys.SE questions on the topic of zero modes. Such as, e.g., zero-modes (What are zero modes?, Can massive fermions have zero modes?), majorana-zero-modes (Majorana zero ...
4
votes
0answers
75 views

3d Ising Fixed point on general space manifold?

The headline question: Is it known how to construct an equivalent of the 3-D Ising Fixed point theory on an arbitrary 3-D manifold? Or any non-trivial d > 2 fixed point? The answer is maybe as simple ...
3
votes
1answer
83 views

Full calculation of B meson mixing amplitude

I am trying to calculate B mixing in the Standard Model (in preparation to go beyond the SM). I have no trouble doing the gamma matrix algebra etc. but the loop integral keeps tripping me up. In my ...
6
votes
2answers
616 views

The phrase “Trace Anomaly” seems to be used in two different ways. What's the relation between the two?

I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing. The first way I've seen it used is in the manner, for ...
7
votes
1answer
173 views

What are renormalons from a physics point of view?

This is again a question in the context of this paper about the Exact Renormalization Group. On p 23 and the following few pages, it is explained that for a $\lambda \phi^4$ bare action at the bare ...
2
votes
1answer
122 views

How to justify matter-field interaction for non-gauge-invariant Hamiltonian?

I'm wondering how can one formally justify the electromagnetic response of a system which does not verify local U(1) gauge invariance. A good example of what I would like to consider is given by the ...
5
votes
0answers
137 views

Holographic Field Theory

I am trying to read this paper http://arxiv.org/abs/1204.1780 and I don't understand how to get from eqn 91 which is, $$S_{2} = N^{2} \{V[P^{(1)}_{m}] + (J^{(1)m} - \mathcal{J}^{m})P_{m}^{(1)}\} ...
4
votes
0answers
318 views

Toward the establishment of non-equilibrium (quasi-equilibrium) magnon BEC theory

In 2006, Demokritov et al have reported that they have achieved the observation of quasi-equilibrium magnon Bose-Einstein condensation (BEC) in YIG at finite (room) temperature by using the method ...
2
votes
0answers
144 views

Field content and symmetry groups of Minimal Composite Higgs Models

I'm trying to teach myself the Composite Higgs Model, both its theory and its LHC phenomenology (particularly the 4DCHM). Unfortunately, I'm struggling; the literature is contradictory and/or omits ...
3
votes
1answer
115 views

Transformation law for fermionic measure in functional integral

I am reading the paper "Bosonization in a Two-Dimensional Riemann-Cartan Geometry", Il Nuovo Cimento B Series 11 11 Marzo 1987, Volume 98, Issue 1, pp 25-36, ...
24
votes
1answer
610 views

Sigma Models on Riemann Surfaces

I'm interested in knowing whether sigma models with an $n$-sheeted Riemann surface as the target space have been considered in the literature. To be explicit, these would have the action ...
3
votes
0answers
136 views

Can mass dimension of a field be viewed as another 'quantum number'?

While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ...
5
votes
0answers
102 views

Finding symmetry of a part of an equation, given the group transformation property of another part

I am reading this paper on Dyons and Duality in $\mathcal{N}=4$ super-symmetric gauge theory. The author finds the zero modes or a dirac equation obtained by considering first order perturbations to ...
13
votes
5answers
1k views

Reading list in topological QFT

I'm interested in learning about topological QFT including Chern Simons theory, Jones polynomial, Donaldson theory and Floer homology - basically the kind of things Witten worked on in the 80s. I'm ...
3
votes
2answers
251 views

Why is fractional statistics and non-Abelian common for fractional charges?

Why non integer spins obey Fermi statistics? Why is fractional statistics and non-Abelian common for fractional charges?
10
votes
2answers
439 views

How can we define BF theory on a general 4-manifold?

(I have rewritten the question some, with new understanding) 4d BF theory is classically presented as the TFT arising from the Lagrangian $B\wedge F$, where $B$ is an abelian 2-connection (locally ...
6
votes
1answer
180 views

Two-loop regularization

Working out some quantum field theory computations, I have to find out the value of the two-loop Feynman integral $$ ...
10
votes
2answers
332 views

How do you simulate chiral gauge theories on a computer?

David Tong and Lubos Motl have argued that our universe can't possibly be a digital computer simulation because chiral gauge theories can't be discretized, and the Standard Model is a chiral gauge ...
13
votes
4answers
892 views

Is there an intuitive description of vacuum entanglement?

People often refer to the fact that the vacuum is an entangled state (It's even described as a maximally entangled state). I was trying to get a feeling for what that really means. The problem is ...
6
votes
3answers
828 views

Why can't gauge bosons have mass?

Clearly, a mass term for a vector field would render the Lagrangian not gauge-invariant, but what are the consequences of this? Gauge invariance is supposed to be crucial for the renormalisation of a ...
8
votes
2answers
749 views

Majorana zero mode in quantum field theory

Recently, Majorana zero mode becomes very hot in condensed matter physics. I remember there was a lot of study of fermion zero mode in quantum field theory, where advanced math, such as index ...
6
votes
1answer
871 views

What is the relationship between string net theory and string / M-theory?

I've just learned from this one of Prof. Wen's answers that there exists a theory called string net theory. Since I've never heard about this before it picks my curiosity, so I`d like to ask some ...
11
votes
3answers
552 views

Is there any quantum-gravity theory that has flat space-time and gravitons?

Many quantum-gravity theories are strongly interacting. It is not clear if they produce the gravity as we know it at low energies. So I wonder, is there any quantum-gravity theory that a) is a well ...
5
votes
2answers
307 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 ...
8
votes
1answer
172 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 ...
5
votes
2answers
244 views

Poincare Symmetry in QFT

Given that spacetime is not affine Minkowskispace, it does of course not possess Poincare symmetry. It is still sensible to speak of rotations and translations (parallel transport), but instead of ...
6
votes
2answers
148 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 ...
3
votes
3answers
115 views

QED as a Wightman theory of observable fields? With a collision theory?

[Note: I'm using QED as a simple example, despite having heard that it is unlikely to exist. I'm happy to confine the question to perturbation theory.] The quantized Aᵘ and ψ fields are non-unique ...
10
votes
1answer
374 views

What are the limitations of the superspace formalism?

Just from reading this slightly technical introduction to supersymmetry and watching these Lenny Susskind lectures, I thought that the Lagrangean of any "reasonable" supersymmetric theory can always ...
2
votes
0answers
77 views

Why/When can the gauge superfield and/or chiral superfield kinetic term in $(2,2)$ SUSY be ignored?

This is in reference to the argument given towards the end of page $61$ of this review paper. There for the path-integral argument to work the author clearly needed some argument to be able to ignore ...
7
votes
2answers
153 views

Could motives aid in the study of the Navier-Stokes equations?

Recently, mathematicians and theoretical physicists have been studying Quantum Field Theory (and renormalization in particular) by means of abstract geometrical objects called motives. Amongst these ...
6
votes
1answer
385 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 ...