Questions tagged [effective-field-theory]

An effective field theory is a systematic approximation for an underlying quantum field theory or a statistical model that includes the appropriate degrees of freedom of phenomena occurring at a chosen length scale (or energy scale), while ignoring substructure and degrees of freedom at shorter distances (or higher energies), summarizing those in its parameters.

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Heirarchy problem

Can anyone explain the hierarchy problem in context to Higgs mass corrections by scalar loop and fermion loop (the problem arising when we try to treat SM as an EFT)? and how do these corrections ...
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Effective Field Theories of QCD

Recently, I am studying the online course Effective Field Theory provided by MIT OCW. Prof. Stewart gives a nice picture to summarize the effective theories: As a newbie in this field (I only have a ...
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Feynman rules for space-dependent coupling

Let's say I have an effective action which looks like (I got this action from large $N$ method for $\varphi^4$ theory): $$\int \frac{d^4x}{2g}\phi^2(x)+\int d^4x \ \log(-\nabla^2+\mu^2+i\phi(x)). $$ ...
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How can one derive Schwarzian derivative action as low energy effective field theory invariant under global $SL(2,\mathbb{R})$?

In a recent paper (page 47, below eq (4.173)) they make a passing claim that the Schwarzian derivative action can be derived using effective low energy field theory reasoning. I imagine they mean that ...
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Projecting out interactions with high-energy states

I have a single-particle Hamiltonian with a discrete energy spectrum $E_{n,k}$ with two degrees of freedom, $n=0,1,2,3...\infty$ and $k$ which has only a few possible values. $E_{n,k_1}$ and $E_{n,k_2}...
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Where the derivative corrections come from in Wilson renormalization?

I known that in the Wilson renormalization process fast modes are integrated out in order to define an effective action for the low modes field. Considering phi to the fourth theory it's easy to see ...
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Antisymmetric matrices in effective field theory

I'm trying to construct a nonlinear $d$-dimensional version E&M as an effective field theory. Let $F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$ be the field strength. The most general action ...
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Does every regularization/renormalization approach gives running coupling constants?

I'm studying different tools for regularization and renormalization. Until now I vaguely understand 1) the wilson approach to renormalization where one thinks of the theory as essencially effective ...
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Lagrangians in field theory and ignorance

The thing that has always bothered me while taking my QFT course was the seemingly arbitrary nature of Lagrangians. For the Klein Gordon equation we just wrote down the simplest Lorentz invariant ...
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How do Graviton-based theories of gravity explain the expansion of the universe?

In General Relativity, the expansion of the universe is modeled using the Friedmann–Lemaître–Robertson–Walker metric, and the expansion itself is a metric expansion by which the scale of space itself ...
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Marginal interactions for Fermi surfaces

I am struggling to understand Polchinski’s derivation (https://arxiv.org/abs/hep-th/9210046) of the conditions for marginality of the 4-fermi operator. For a scattering process $(\mathbf{p}_1,\mathbf{...
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What is the Wilsonian definition of renormalizability?

In chapter 23.6, Schwartz's quantum field theory book defines renormalizability as follows, paraphrasing a bit for brevity: Consider a given subset $S$ of the operators and its complement $\bar{S}$....
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Wavefunction Renormalization in Wess-Zumino Model

In Modern Supersymmetry: Dynamics and Duality, on page 134 and 135 in section 8.2, the authors studied the wavefunction renormalization of the Wess-Zumino model. The kinetic terms are given by $$\...
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Why do irrelevant operators require infinitely many counterterms?

As far as I understand it, in the Wilsonian picture of renormalization, we view a theory as having some fixed cutoff and bare couplings, and integrate out high-momentum modes to understand what ...
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295 views

Relevant interaction terms based on dimension of coupling constants in quantum field theory

For a $\phi^{3}$ quantum field theory, the interaction term is $\displaystyle{\frac{g}{3!}\phi^{3}}$, where $g$ is the coupling constant. The mass dimension of the coupling constant $g$ is $1$ in 4D, ...
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How is the chiral condensate estimated from the pion decay constant?

In low-energy QCD, there are several dimensionful quantities that come up. Writing the chiral condensate as $$\langle \Omega | \bar{q}_{Ri} q_{Lj} | \Omega \rangle = - v^3 \exp \left(\frac{2 i \pi^a(...
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Piecewise solution to Euler-Lagrange equations in effective field theory

I would like to consider a background for a quantum field theory made up by connecting continuously two different solutions of the Euler Lagrange equations. The problem is one dimensional (let's call ...
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What happens to the (Wilsonian) effective action if a symmetry is spontaneously broken?

A spontaneously broken symmetry is a symmetry of the action which does not manifest itself in physical states. Since the action is still invariant under this symmetry, can we say the same about the ...
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${\cal N} = 1$ SUSY Non-renormalization theorem

In Ref. 1, on Page 53, the ${\cal N} = 1$ SUSY non-renormalization theorem is derived. One first specifies the symmetries of the general ${\cal N} = 1$ SUSY action in the superspace formalism, and ...
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Renormalisation group flow of the $\phi^4$ theory

I am reading Peskin & Schroeder about the renormalisation group flow of the $\phi^4$ theory: $${\cal L} = \frac{1}{2}(\partial_\mu\phi)^2 +\frac{1}{2}m^2\phi^2 + \frac{\lambda}{4!}\phi^4 $$ P &...
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Non-trivial content of AdS/CFT for a generic EFT on AdS

I have a very generic and naive question on the actual content (and usefulness) of the AdS/CFT conjecture in the low energy approximation where one considers a low energy QFT on AdS, comprising ...
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IIB Supergravity from worldsheet (super)conformal invariance of Green-Schwarz string

After reading this question How are low energy effective actions derived in string theory? I began to wonder what is the coupling of the string to the other sugra fields. In almost all textbooks ...
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Are Instantons Massless?

That is, are the only field configurations which give a non-zero winding number ones in which the Fourier transform includes a factor like $\theta(k^0)\hat{D}\delta(k^2)$, where $\hat{D}$ is some ...
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Does the Flavor symmetry forbid $uu\rightarrow cc,ss$?

This question comes from the reading of this paper. They suppose a flavor symmetry group $G_F = U(3)_q\times U(3)_{d} \times U(2)_{d}$ which acts on the three LH quarks $q_L$, three RH quarks $u_R$ ...
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Size of quantum corrections at infinity

Suppose we have a one dimensional field theory for the field $\phi(r)\;r\in[0,\infty]$ and that the solution for the background (Euler Lagrange equations) give a function $\phi_0$ that goes to a ...
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Is Hilbert-Einstein action just the leading order of some kind of series?

Introducing the action for the gravitational field my GR professor stated that, in principle, one could write it as $$S = k\int d^4x\sqrt{g}(\sum_n\sum_m a_{nm} R_n^m - 2\Lambda), \space \space \...
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Is the effective Lagrangian the bare Lagrangian?

In standard (non-Wilsonian) renormalization we split the bare Lagrangian $\mathcal{L}_0$ into a physical Lagrangian $\mathcal{L}_p$ with measurable couplings and masses counterterms $\mathcal{L}_{...
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Effective Lagrangians

I get the impression from reading, e.g., this paper, that the term "effective Lagrangian" refers to a Lagrangian derived from a Taylor series expansion of an arbitrary function of known invariants. ...
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Understanding irrelevant operators in Wilsonian RG

I had always understood irrelevant operators as operators whose coefficients got smaller at lower energy scales, but there's a passage from Schwartz's Quantum Field Theory and the Standard Model which ...
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How does the generalized effective action in Wetterich's exact RG scheme relate to observables at different scales?

I am not familiar with Wetterich's exact RG paradigm, and cannot understand the main idea behind it. I understand that if one could have solved the model and obtained the all the n-point functions ...
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Unit of pion-decay constant

In the natural unit system, the pion-decay constant $f_{\pi}$ is $92.4\:\rm MeV$. But I think that a decay constant should have a dimension of $[T]^{-1}$, where $[T]$ is the dimension of time. Then, ...
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Effective field theories from QCD

Is there a way - at least formally - to derive theories like chiral perturbation theory or heavy baryon effective theory from QCD? As an example: is it possible first to introduce the effective ...
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What is a superfluid in field theoretic terms?

I'm wondering how one precisely defines a superfluid in terms of the effective field theory description. In Nicolis's paper http://arxiv.org/abs/1108.2513 there seems to be an extremely simple ...
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A pedestrian explanation of Renormalization Groups - from QED to classical field theories

shortly after the invention of quantum electrodynamics, one discovered that the theory had some very bad properties. It took twenty years to discover that certain infinities could be overcome by a ...
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Why does the Lagrangian Density have to be a polynomial of the field?

In a lecture, a professor appeared to have said that the Lagrangian can only contain terms that have powers of $\phi$ and a term with $\partial_\mu \partial^\mu \phi$ . I imagine this would make any ...
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Why do we care about old-style, counterterm renormalizability?

There are a few different definitions of renormalizability that are standard in quantum field theory textbooks. They're all called the same thing, but I'll make up names to make the distinctions clear....
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Calculation of Wilson Coefficients

In Flavour physics, amplitude of decay processes is generally expressed in terms of effective operators (reference). In the framework of effective field theory amplitude $\propto C_iO_i$, where $O_i$ ...
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Why is the standard model renormalizable if we believe it is an effective theory? [duplicate]

We believe that the standard model is only an effective field theory of its true UV completion. However, effective theories have dimensionful couplings and are not renormalizable. The standard model ...
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High-energy effective field theory

Usually when one speaks of effective field theories, one is looking to integrate out certain fields which are typically heavy in comparison to the regime of interest. That is one has a theory at a ...
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How to fuse quantum mechanics and general relativity?

I am very new to this topic but I have started reading Kevin Wray's lecture notes about string theory (PDF) and in the introduction he says: "Sometimes it is said that we don’t understand how to ...
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Computing the Wilsonian Action

Equation 12.5 of Peskin&Schroeder reads $$Z = \int\left[\mathcal{D}{\phi}\right] e ^{-\int d^dx \, \frac{1}{2} (\partial \phi)^2 + \frac{m^2}{2}\phi^2 + \frac{\lambda}{4!}\phi^4} \cdot \...
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Finding the effective Hamiltonian in a certain subspace

In order to find the effective Hamiltonian in a subspace which is energetically well separated from the rest of the Hilbert space people try to find a unitary transformation which makes the ...
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Recovering nonrelativistic quantum mechanics from quantum field theory

In quantum field theory -- specially when applied to high energy physics -- we see that the requirements of Lorentz invariance, gauge invariance, and renormalizability strongly limit the kinds of ...
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Why is vanishing beta function associated with scale-invariance?

Why is vanishing beta function associated with scale-invariance? Coupling constants have change rate of zero at some scale, but how is that related to scale-invariance? Association of vanishing beta ...
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Symmetries of effective field theory of hydrodynamics: a confusing calculation

This is a very specific question about a paper by P. Glorioso and H. Liu that can be found here https://arxiv.org/pdf/1805.09331.pdf. In particular I want to understand how the authors get from the ...
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Wilsonian RG approach to Fermi liquid theory

In modern terms, Landau's theory of Fermi liquids is understood as the fixed point of a Wilsonian RG as one scales towards the Fermi surface. Shankar and others use the RG interpretation to explain ...
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Is there any threat to the results of our effective field theories from unknown higher energy theories?

We use renormalization arguments (and experiments) to change the couplings of a theory and suppress the higher energy physics (saying things like “whatever the fundamental theory, this will be true of ...
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Can a unified physics theory have a smaller number of couplings than its effective field theory?

Suppose that we have a QFT that has $n$ number of physical coupling constants, or there are $n$ coupling constants required to perturbatively renormalize the given QFT. Suppose this QFT to be an ...
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QED vertex correction, proper vertex function and meaning

I might be making great confusion in trying to interpret proper vertex function. I'm studying QED vertex correction. I'm just going to write down the pieces of the puzzle. So I know that the ...
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Comparing momentum cutoff and lattice regularization in Quantum Field Theory

Usually, it is heuristic to say that we can understand a QFT with a momentum cutoff $|k|<\Lambda$ by imagining that the system is living on a lattice. I would like to ask: (1) Is there any ...