A postulated symmetry between bosonic and fermionic fields in quantum field theories and string theories.

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Construction of $\mathcal O(-1) \oplus \mathcal O(-1)$ over $CP^1$ [closed]

First, Consider a $\phi$ as a coordinates on a copy of $Z= C^N$ Then, I know \begin{align} |\phi_1|^2 + |\phi_2|^2 + \cdots |\phi_N|^2 = r \end{align} which describe $S^{2N-1}$. Implementing $U(1)$ ...
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35 views

Supersymmetry breaking and normalizable zero modes

Why does supersymmetry always lead to normalizable zero modes? For example, it is stated in the paper by Michelson and Kaplan (http://arxiv.org/abs/hep-th/9510053) that we can assume, without loss of ...
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77 views

Jim Gates' discovery of error-correcting codes in equations of supersymmetry

Can anyone explain what's going on here, in a way that isn't just a lot of gee-whiz? Here's the arXiv article. I'm more of a computer science person than a physicist, so error-correcting codes are ...
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35 views

Chiral multiplet : Fundamental and adjoint representation and its Lagrangian

In supersymmetry theory, consider $4d$ $N=1$ theory, we know that chiral superfield (In fundamental representation $\Phi \rightarrow e^{i\alpha} \Phi$) $\Phi$ and its lagrangian is given as ...
6
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259 views

Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
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128 views

Intuition behind Nekreasov's instanton partition function. What do the partitions represent exactly?

I am struggling to understand many things behind Nekrasov's solution. Firstly I want to understand the following In this theory, $a$ represents VEVs the Higgs scalar. So, is the gauge field of the ...
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37 views

M-theory compactified on $S^4$

I am trying to understand what happens to the 32 supersymmetries of M-theory when it is compactified on $S^4$, with the other seven dimensions being flat, e.g., $\mathbb{R^7}$, $\mathbb{R^6} \times ...
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9 views

How can we reduce the number of necessary parameter to 19 in phenomenological Minimal Supersymmetric Standard Model (pMSSM)?

I am very new in SUSY and I heard something about pMSSM. Question is that how we can reduce the number of necessary parameter to 19 in pMSSM. If you have any suggestion as a brief introduction or any ...
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41 views

What is the importance of $2d$ supersymmetric gauge theory? [closed]

I have been working $2d$ $N=(2,2)$ theories focused on checking duality like, Seiberg duality (2d version: named "Hori-Tong" duality) and its extension. During the study i got $2d$ $N=(2,2)$ ...
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1answer
36 views

Question about Supermatrix algebra

This question is inspired from a reading of Appendix F of P. van Nieuwenhuizen, Supergravity, Phys. Rep. 68 (1981) pp. 369-374. Consider a "supermatrix" $$M = \left(\begin{array}{cc} A & B\\ C ...
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28 views

Lagrangian for $\mathcal{N}=4$ SQED in 3D

What is the Lagrangian for $3D$ $\mathcal{N}=4$ supersymmetric QED, with $N_f$ hypermultiplets? In particular, which is the form of the Fayet-Iliopulos terms, and the real mass terms?
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48 views

M5 brane zero modes

The Euclidean M5 brane worldvolume has an anti self-dual 3-form and two negative chirality spinors. The spinors can couple to the SO(5) gauge fields of the normal bundle, but the 3-form cannot couple ...
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96 views

Pole in reflection/transmission coefficient and bound states

I was working on a scattering problem in a quantum mechanical system with Hamiltonian $$H_1=A^{\dagger}A=(-\partial_x+W(x))((\partial_x+W(x))).$$ One can show that a 'supersymmetric' partner to this ...
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28 views

N=4 d=3 susy algebra

Does anybody know how to derive the $\mathcal{N}=4$ d=3 susy algebra doing a dimensional reduction from the most famous $\mathcal{N}=4$ d=4? Equivalently, does it exist a reference in the literature ...
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28 views

The BPS mass formula for 3d N=4

Is the mass formula (or equivalently the central charge formula) known for BPS particles in 3d $\mathcal{N}=4$ susy gauge theories? In particular, what is its dependence on the Fayet-Iliopoulos ...
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1answer
64 views

Meaning of Supersymmetry

Supersymmetry is a relation between bosons and fermions. Based on this definition, what is the meaning of "number of supersymmetries"?
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33 views

What are the global symmetries of $\mathcal{N}=2$ SYM before twisting and after twisting?

I am confused with the global symmetries of $\mathcal{N}=2$ SYM. On one hand I know that the theory has a $U(2)_R = SU(2)_R \times U(1)_R$ symmetry. Now, there exists also a $U(1)_B$ global symmetry. ...
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32 views

Diiference between three squashed sphere and three sphere and number of susy

First I know that three sphere $S^3$ and squashed sphere $S_b^3$ \begin{align} S_{b}^{3} = \begin{array} & R^2 \times S_{r}, \quad r=b, \quad b\rightarrow 0 \\ R^2 \times S_{r}, \quad ...
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45 views

Hypermultiplet as BPS particles

In the third paragraph of page 7 of the paper arxiv:1112.3984 it mentions that we form a basis out of hypermultiplets on the charge lattice $\Gamma$. My questions are: In what sense do we form such ...
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54 views

Concerning topology of BPS states of the M5-brane

My question is about the M5-brane in M-theory. I would like to know whether the BPS states of the M5-brane worldvolume theory (especially the 1/2 BPS and 1/4 BPS ones) are independent of the topology ...
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146 views

Can pure-bosonic string theories exist in curved spacetime?

Question: Can there be a consistent non-supersymmetric pure-bosonic string theory in some curved spacetimes? Reason: Since fields with certain amount of negative mass can exist in curved spacetime ...
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0answers
33 views

Can we have supersymmetry using real scalar instead of complex scalars?

I am aware that a suersymmetric theories containing a complex scalar a Weyl fermion and an auxiliary field exist. I was wondering if we can have something analogous using real and not complex scalar ...
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1answer
81 views

Calabi Yau Motivation

I have just begin to study Calabi Yau compactification. Looking in many book I found that, if we start with a critical superstring theory in $D=10$, we are in search of a compact $D=6$ Calabi Yau ...
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70 views

Anomaly polynomial of Hitchin system $\mathcal{N}=2$ 4d SQFT

I would like to ask about mathematical background of this object. So, I am trying to puzzle out with 4d $\mathcal{N}=2$ SQFT. As far as I can gather this theory can be described in terms of ...
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1answer
96 views

Canonical spinors from gauge transformations

In this 2006 paper, http://arxiv.org/abs/hep-th/0610128, there is the concept of gauge transformation and how was it employed that I do not fully understand. Note, what will be talked about below is ...
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1answer
140 views

Where does the “Supersymmetry” in Witten's proof of the Morse inequalities come from?

Where does the "Supersymmetry" in Witten's proof of the Morse inequalities (original paper and outline of proof for mathematicians) come from? Hopefully someone can provide an intuitive understanding? ...
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53 views

Representation theory and the Nekrasov partition function

Is there any review or lecture notes on the Nekrasov partition function which particularly thinks of this from a representation theorist's point of view? Some possibly related references I know of ...
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72 views

Supersymmetric transformation of general Wess-Zumino Lagrangian

I suspect that I might have understood something wrong here. I'm trying to show that the general Wess-Zumino Lagrangian \begin{align} \mathcal{L} &= \int d^2\theta d^2\bar{\theta} K(\Phi^*, \Phi) ...
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42 views

Can i use the $y^*$ representation of the chiral covariant derivatives on a superfield that contains both $y$ and $y^*$?

Imagine I want to compute this $$D^{\dagger2}D_{\alpha}(\Phi^*\Phi)$$ where the $D$-s are super-covariant derivatives and $\Phi$ is a chiral superfield. Following the notation of this review on ...
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1answer
70 views

Dimensional reduction of SUSY theories

I know that if one reduces 10 dimensional $\mathcal{N}=1$ SYM theory to 4 dimensions one gets $\mathcal{N}=4$ SYM. There are other examples also. I have two related questions regarding this fact. ...
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24 views

Which is the analogous of the unitarity constraint of chiral perturbation theory in superchiral perturbation theory?

I am trying to reconstruct something and I would appreciate omeone helping me filling the gaps. To motivate my question let's first consider chiral perturbation theory with up and down quarks. This is ...
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52 views

Supersymmetric chiral QCD resource recommendations?

I want somebody to recommend me where I can read about supersymmetric chiral QCD.
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80 views

Projective superspace: why extra bosonic coordinates

I'm studying the projective superspace formalism for N = 4 supersymmetric $\sigma$-models in two dimensions. My question is: why do we need the extra bosonic coordinates for the manifest action? I ...
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1answer
79 views

Why must superpartners have the same gauge quantum numbers?

The title leaves it quite clear, why must superpartners have the same gauge quantum numbers?
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1answer
129 views

Should the (On-shell) (2+1)d $N=2$ Chiral Multiplet Contain Two Scalars and Two Majorana Spinors?

In supermultiplets, the bosonic degrees of freedom and the fermionic degrees of freedom need to match in number. The number of degrees of freedom of a field corresponds to the number of independent ...
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75 views

(Super)Gauge Fixing in Supersymmetry

I have three questions about gauge fixing in supersymmetry, one is general and the other two explicit: Why gauge fixing seems not important in supersymmetry? By "not important" I mean gauge fixing ...
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56 views

Projection that keeps graviton but gets rid of B-field

We consider the closed superstring and the massless states in the (NS,NS)-sector \begin{equation} \tilde{b}^i_{-\frac{1}{2}} |0\rangle_L \otimes b^j_{-\frac{1}{2}} |0\rangle_R. \end{equation} It is ...
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1answer
118 views

Quantum mechanic particle

In non relativistic quantum mechanic, we are dealing with a problem involving a particle in one dimensional space, and it has been given the potential and it reads: ...
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1answer
50 views

Polchinski, (0,0) picture vertex operator

I am currently working through chapter 12 of Polchinski and am confused as to how the equation $(12.3.39)$ for the (0,0) picture vertex operator arises. From the text: The state–operator mapping ...
6
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1answer
230 views

Invariance of supersymmetric Yang-Mills theory under supersymmetry

I was following Brink, Scherk and Schwartz, "Supersymmetric Yang-Mills theories". The variation of the Lagrangian w.r.t a supersymmetry transformation can be reduced to $$ \delta L = -igf_{a b c} ...
2
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1answer
63 views

What is $\mathcal{N}=2$ QED?

I would like to know is $\mathcal{N}=2$ QED is simply a $\mathcal{N}=2$ theory with gauge group $U(1)$ like in normal QED? If not, exactly what theory is it? Is there some reference for it?
2
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1answer
202 views

Signs of supersymmetry and thus dark matter at CERN

The Large Hadron Collider at CERN has just re-started after a two year pause and is now running at unprecedented levels of 6.5 TeV, with collisions that will release up to 13.5 TeV. With this increase ...
2
votes
1answer
181 views

Understanding Fierz rearrangement identity

I'm trying to get a better grasp of the Fierz rearrangement identity for 2-component spinors (Equation 2.20 I'll be using the Van der Waerden notionation used in the given link) $$ \chi_\alpha (\xi ...
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1answer
76 views

What is meant by “the superpotential is not renormalized”?

Reading about supersymmetry I often read the phrase because of the non-renormalization theorems the superpotential is not renormalized. I would like someone to be more explicit on what is ...
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1answer
83 views

Do the Grassmann coordinates in the superfield formalism have any physical meaning?

In the superfield formalism we consider fields in a space who has four so called bosonic coordinates $x^{\nu}$ and four so called fermionic coordinates ...
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1answer
64 views

Partial derivatives of chiral superfields with respect to scalar components in the superpotential

I am following some notes on supersymmetry by Matteo Bertolini and I need some clarification. Chapter five deals with sypersymmetric Lagrangians and the superpotential is introduced. It is stated ...
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71 views

Supermultiplet dimensions from Young Tableaus

In John Terning's book, on pages 14 and 15, there are lists of $\mathcal{N} = 2$ and $\mathcal{N} = 4$ supermultiplets, labeled in terms of the dimensions of the corresponding R-symmetry $d_R$ and ...
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1answer
94 views

Why must the supersymmetry generators be spinors?

I have read in a few places (for example, at page 5 here) that the supersymmetry generators must be spinors. Quoting the reference mentioned The generator of the symmetry must relate two types of ...
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1answer
80 views

Elementary question about global supersymmetry of a worldsheet [closed]

I'm reading chapter 4 of the book by Green, Schwarz and Witten. They consider an action $$ S = -\frac{1}{2\pi} \int d^2 \sigma \left( \partial_\alpha X^\mu \partial^\alpha X_\mu - i \bar \psi^\mu ...
2
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1answer
143 views

With the LHC about to restart as max energy, are there absolutely no hints or tantalizing signs of Supersymmetry in previous data?

Over the last couple of years I've seen several articles talk about hints or bumps in the data that might point to Supersymmetry. An article in NewScientist from Summer 2012 discussed the discovery of ...