# Tagged Questions

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### Converting two component product to four component notation

Consider the product of two left Weyl spinors in the notation commonly found in supersymmetry, \chi ^\alpha\eta_\alpha = \chi ^\alpha \epsilon _{ \alpha \beta } \eta ^\beta ...
66 views

### Deriving Feynman rules from a Lagrangian for vertex factors for “more complicated” interactions

I am trying to derive Feynman rules from a given Lagrangian and I got stuck on some vertex factors. What for example is the vertex factor that corresponds to the four-scalar interaction that is ...
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### Supersymmetric cancellation of loop contributions in a SUSY gauge theory

It is known that in SUSY models, loop contributions are automatically zero leading to a technically natural solution of the Higgs mass hierarchy problem. In many SUSY books/notes, it is often shown ...
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### Finite corrections to the Higgs mass in SUSY

I am worried here about specific supersymmetric scenarios in which an energy scale above the TeV is introduces. An example would be the Seesaw extension of the Minimal Supersymmetric Standard Model. ...
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### Majorana Superfields

so apologies if this is a silly question... In the type 1 see saw model we add extra Majorana fermions to our model. These fermions have to be total gauge singlets in order to have a Majorana mass ...
113 views

### How do I deal with a quantum field in the denominator?

I am wondering how to deal with an expression like $$\int d^4\theta \frac{1}{T + T^\dagger} \big( \dots \big)$$ If the denominator was of the form $1 + T + T^\dagger$, I could assume that $T \ll 1$ ...
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### A question about Feynman diagram and symmetry factor

Consider a $\varphi^3$ theory: $$Z_1(J) \propto \exp\left[\frac{i}{6} Z_g g\int \mathrm{d}^4 x \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right] Z_0(J),$$ where  Z_0(J) = ...
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### Can symmetry generators anticommute with the S-matrix?

In Coleman and Mandula's proof of the Coleman-Mandula theorem, they define a symmetry transformation as an unitary $U$ which, turns one-particle states into one-particle states, acts on ...
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### Is there a soft Goldstino theorem?

For ordinary spontaneously broken symmetries, you can demonstrate relations between S-matrix elements with a soft goldstone emission and another S-matrix element without the emission. If I break ...
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### why do the electroweak vacuum have to be charge and color neutral?

My question is why the electroweak vacuum of the Standard Model have to electroweak charge and QCD color neutral? What goes wrong if electroweak vacuum has either non-zero charge or color quantum ...
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### Assumptions of the Coleman-Mandula Theorem

In the original paper All Possible Symmetries of the S-Matrix, by S. Coleman and J. Mandula, they prove their famous 'no go' theorem regarding the possible extensions of PoincarĂ© symmetry. The ...
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### What's the Coulomb Branch and why is it important?

I'm studying the introduction of flavour degrees of freedom in the AdS/CFT correspondence and now I'm supposed to calculate the mass spectrum of mesons in the Coulomb branch. I have searched the ...
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### Do exact beta functions exist in (super)gravity theories and string theory?

An exact beta function exists for Super-Yang-Mills theories in 4D without matter - the so-called NSVZ beta function. Does a similar exact beta-function exist in gravity or supergravity theories? In ...
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### Gossip in Physics

Given, $M_4 = \Sigma \times C$, How do you get an effective theory by studying maps $\Sigma \rightarrow M_4$ . Technically, the physics in one manifold is supposed to gossip about the ...
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### Feynman Diagrams in 2 component notation

When using two component notation people often prefer to refrain from using arrows in Feynman diagrams to denote charge flow as is done in four-component notation. Instead, if understand correctly, ...
150 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 ...
36 views

### Twisted supermultiplets

What is a twisted supermultiplet, in a generic supersymmetric theory? Which ordinary fields belong to one of such twisted supermultiplets? I am confident with the idea of a supermultiplet or a ...
184 views

### Why must SUSY be broken?

Background One usually claims that supersymmetry must be spontaneously broken. The reasoning is roughly the following: Since $M^2=P^{\mu}P_{\mu}$ is a casimir operator of the supersymmetry algebra, ...
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### Coleman-Mandula theorem in mathematical language

Every supersymmetry text starts off mentioning the Coleman-Mandula theorem. Often it is introduced using rather colloquial terminology. I was wondering if anyone knew a precise mathematical ...
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### Dual photon in d=3

In some papers (such as http://arxiv.org/abs/hep-th/9910184 and http://arxiv.org/find/all/1/all:+AND+kapustin+AND+topological+disorder/0/1/0/all/0/1) I am reading it is always referred at "the dual ...
48 views

### stress tensor in Kazama-Suzuki construction

This is a technical question about equation (2.42) of the original paper [KS] of the Kazama-Suzuki construction. I think the authors did a simple substitution ...
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### $\mathcal{N}=4$ SUSY in $d=3$ versus $\mathcal{N}=2$ in $d=4$

Which is the field content of the hypermultiplet and the vector multiplet in $\mathcal{N}=4 \ d=3$ Supersymmmetry? Is it correct to state that $\mathcal{N}=4$ in $d=3$ has $8$ supercharges, (since ...
148 views

### Negative sign in the Dirac term from the SUSY Kahler potential

I want to calculate the Dirac term from the canonical Kahler potential, $$K = \Phi ^\ast \Phi \tag{1}$$ but I'm coming across a pesky negative sign in the final result. I ...
83 views

### Generalized Unitarity cut of Scalar One-loop Box integral

How does one perform the integrals in four particle cuts in generalized unitarity? It would be helpful how one finds solutions to the simplest case, the fully determined box integral given by: ...
134 views

### Supersymmetric generalisation of the bosonic $\sigma$ model in QM

I am reading some lecture notes which demonstrate how various models in SUSY QM can be used to obtain topological invariants such as the Euler characteristic from the Witten Index. The following ...
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### 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 ...
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### What is a supermultiplet?

In Quantum field theory by Lewis H. Ryder, a supermultiplet is mentioned with no explanation as to what one is.
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### How does the electron electric dipole moment (EDM) depend on supersymmetry?

I have read a recent paper that says that limit on the EDM of the electron has now been measured to 12 times better accuracy. According to that paper, as I understood, there should be a difference in ...
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### Moduli Space of $\mathcal{N}=4$ SYM on $\mathbb{R} \times S^3$

When we define $\mathcal{N}=4$ SYM on flat Minkowski space, the supersymmetric vacua are parametrized by scalars living in the cartan subalgebra of the gauge group. A generic point in the moduli space ...
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### Why is the R-symmetry in $\mathcal{N}=4$ $SU(4)$ and not $U(4)$?

In $\mathcal{N}=4$ SYM we have 4 supercharges. Naively, I would have thought that the R-symmetry would be $U(4)$. I know that in theories with less SUSY the $U(1)$ can be anomalous. But ...
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### 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 ...
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### How does a SCFT avoid the Haag-Lopuszanski-Sohnius theorem?

According to the Haag-Lopuszanski-Sohnius theorem the most general symmetry that a consistent 4 dimensional field theory can enjoy is supersymmery, seen as an extension of PoincarĂ¨ symmetry, in direct ...
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### Why do three dimensional gauge theories flow to conformal theories in the infrared?

What is meant with the fact that Super Yang-Mills flows to a conformal field theory in the infrared? Also, is this a general fact or does this depend on the fact of considering a certain class of ...
244 views

### Renormalization of Composite Chiral Superfields

On page 24 of these lecture notes http://arxiv.org/abs/hep-th/0309149 it is stated that products of chiral superfields do not suffer from short distance singularities. In other words, if I want to ...
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### Relation between $\mathcal{N}=2$ d=4 SUSY and $\mathcal{N}=4$ d=3 SUSY

What is meant with the fact that supersymmetry with $\mathcal{N}=4$ in three (2+1) dimensions is equivalent to supersymmetry with $\mathcal{N}=2$ in ordinary four (3+1) dimensions? Which way does one ...
106 views

### Hyperkahler manifolds and their use in theoretical physics

Just as the title says: What is the easiest definition of a Hyperkahler Manifold? Could you give some examples of Hyperkahler manifolds, and manifolds which fail to be hyperkahler? Why are such ...
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### Baryon operators for $N_f<N_c$

Simple question. The answer is probably obvious, but I just don't see it. In section 3 of this paper http://arxiv.org/abs/hep-th/9509066 it is stated that in SUSY QCD if $N_f<N_c$ the classical ...
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### What is the relation between N=2 super Yang-Mills and its twist

My question is what is the relation between N=2 super Yang-Mills and its twisted version topological field theory? After twisting N=2 super Yang-Mills, i.e. diagonally embedding $SU(2)'_R$ into ...
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### Why does global supersymmetry commute with gauge transformations?

In particular, I would like to understand the following quotation from a paper by Witten: Nucl.Phys. B188 (1981) 513 (p. 515 at the top) His statement: This is so because in global supersymmetry ...
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### Sharp cut-off, quadratic corrections and naturalness

When introducing the fine-tuning problem, a sharp cut-off as a regulator in the calculation of the Higgs mass corrections is used. Since this regulator breaks translational and gauge invariance, up to ...
247 views

### What is the definition of a “UV-complete” theory?

I would like to know (1) what exactly is a UV-complete theory and (2) what is a confirmatory test of that? Is asymptotic freedom enough to conclude that a theory is UV-complete? Does it become ...
105 views

### Are there two types of D-term and two types of F-term in SUSY?

I've noticed that one can obtain D-terms either by integrating a vector superfield (the vector multiplet) over superspace or by integrating a Kahler potential over superspace. In both cases we get ...
270 views

### Obtaining supergravity from gauging global supersymmetry

On page 92, my still favorite supersymmetry book says, by making the global infinitisimal parameter of a SUSY tranformation spacetitime dependent (gauging) it forces one to introduce a new gauge field ...
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### Do commutation relations exist between superfields?

To quantize a theory, Klein gordon field for example, commutation relations are stablished. Or anticommuting ones in the fermionic case. If I have the Wess.Zumino model or the free model: ...
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### What is the relation between the representation the Higgs field transforms under, the types of couplings in the theory and Higgs/Coulomb branches?

When reading about Higgs and Coulomb 'phases' I came across two separate definitions: The first tells us that the Higgs/Coulomb phases are determined by the representation that the Higgs field ...
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### In spontaneous symmetry breaking, global symmetry broken by gauged subgroup?

My question is simple. Given a group $G$ broken to a subgroup $H$, gauging a possibly different subgroup Hg breaks explicitly the global symmetry $G$, generating what is known as pseudo-Goldstone ...
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### SUSY and the Large hadron collider

Did the LHC rule out SUSY as a solution to the hierarchy problem ? What's the common belief among theorists regarding the possibility of discovering SUSY in the 2015 run of the LHC ? Did the absence ...
212 views

### N=1 v N=2 supermultiplets

I read that the chiral nature of SM fields is an indication that they must be realized in a N=1 supermultiplet (and not N=2). I don't quite understand how so. Please enlighten.
I understand that we can find the energy of a bosonic field in its vacuum state via $E_{vac}^{(B)} = \sum_{\vec{k},s} \frac{1}{2}\hbar\omega_{\vec{k},s}^{(B)}$ and a fermionic one similarly, ...