Landscape

Select a theory SU(2): 4 fund + 4 anti-fund (not completed) SU(2): 1 Adj + 1 fund + 1 anti-fund SU(2): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(2): 1 Adj + 3 fund + 3 anti-fund (not completed) SU(2): 2 Adj SU(2): 2 Adj + 1 fund + 1 anti-fund SU(3): 6 fund + 6 anti-fund (not completed) SU(3): 1 Adj + 1 fund + 1 anti-fund SU(3): 1 Adj + 2 fund + 2 anti-fund (not completed) SU(5): 2 rank-2 symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm + 1 fund + 1 anti-fund SU(5): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 8 anti-fund (not completed) SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm SU(5): 1 Adj + 1 rank-2 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + (conj.) (not completed) SU(5): 1 rank-2 symm + 2 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + (conj.) (not completed) SU(5): 3 rank-2 anti-symm + 1 fund + (conj.) (not completed) SU(5): 1 Adj + 2 rank-2 anti-symm + 2 conj. of rank-2 anti-symm (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm (not completed) SU(5): 2 Adj + 1 anti-symm + 1 conj. of rank-2 anti-symm + 1 fund + 1 anti-fund (not completed) SU(6): 2 rank-2 symm + (conj.) SU(6): 2 rank-2 symm + 1 fund + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + (conj.) SU(6): 1 rank-2 symm + 1 rank-2 anti-symm + 2 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 symm SU(6): 1 Adj + 1 rank-2 symm + 1 conj. of rank-2 anti-symm + 1 fund + 9 anti-fund (not completed) SU(7): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 8 fund (not completed) SU(7): 2 rank-2 symm + 1 fund + (conj.) (not completed) SU(8): 1 rank-2 symm + 2 conj. of rank-2 symm + 1 anti-symm + 9 fund + 1 anti-fund (not completed) SU(9): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 16 anti-fund (not completed) SU(9): 2 rank-2 anti-symm + (conj.) (not completed) SU(9): 2 rank-2 anti-symm + 1 fund (conj.) (not completed) SU(10): 2 rank-2 symm + 2 conj. of rank-2 anti-symm + 1 fund + 17 anti-fund (not completed) SO(5): 5 vector (not completed) SO(5): 1 Adj + 1 vector SO(5): 1 Adj + 2 vector SO(5): 1 rank-2 symm SO(5): 1 rank-2 symm + 1 vector SO(5): 1 rank-2 symm + 2 vector SO(5): 2 Adj (not completed) SO(5): 2 Adj + 1 vector (not completed) SO(7): 1 rank-2 symm + 1 rank-2 anti-symm SO(8): 1 Adj + 1 rank-2 symm + 1 vector (not completed) SO(11): 2 rank-2 symm SO(12): 2 rank-2 symm + 1 vector Sp(2): 1 Adj + 2 fund Sp(2): 1 Adj + 4 fund (not completed) Sp(2): 1 14 + 2 fund Sp(2): 2 Adj Sp(2): 2 Adj + 2 fund (not completed) Sp(2): 1 Adj + 1 rank-2 anti-symm + 2 fund (not completed) Sp(2): 1 Adj + 2 rank-2 anti-symm + 2 fund (not completed) Sp(2): 2 Adj + 1 rank-2 anti-symm + 2 fund (not completed) Sp(2): 1 Adj + 2 rank-2 anti-symm + 8 fund (not completed) Sp(3): 2 Adj + 1 rank-2 anti-symm Sp(3): 3 rank-2 anti-symm + 2 fund (not completed) Sp(4): 3 rank-2 anti-symm (not completed) Sp(4): 3 rank-2 anti-symm + 2 fund (not completed) Sp(4): 2 rank-2 anti-symm + 2 fund (not completed) Sp(4): 2 rank-2 anti-symm (not completed) Sp(4): 2 rank-2 anti-symm + 2 fund (not completed) G2: 1 Adj + 1 fund H0+H1 (not completed) E[USp(6)] (not completed) All theories Data used in arXiv:2408.02953

$a$ =

$c$ =

$\leq a \leq$

$\leq c \leq$

id =

Search for theories with rational R-charges and central charges.

Chosen Fixed Point

Here is the data for the chosen fixed point.
$F_{UV}$ represents the flavor symmetries in the UV Lagrangian, and $F_{IR}$ represents the flavor symmetries in the IR. $F_{UV}$ and $F_{IR}$ can differ due to accidental symmetry enhancement.
The number of marginal operators, $n_{marginal}$, minus the dimension of flavor symmetries in IR, $|F_{IR}|$, corresponds to the coefficient of $t^6$ in the superconformal index.

#	Theory	Superpotential	Central charge $a$	Central charge $c$	Ratio $a/c$	Matter field: $R$-charge	U(1) part of $F_{UV}$	Rank of $F_{UV}$	Rational
295	SU2adj1nf2	${}\phi_{1}q_{1}q_{2}$ + ${ }M_{1}q_{1}\tilde{q}_{1}$ + ${ }M_{2}\phi_{1}\tilde{q}_{2}^{2}$ + ${ }M_{1}M_{2}$ + ${ }M_{1}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{3}\phi_{1}\tilde{q}_{1}^{2}$	0.5069	0.6453	0.7855	[M:[1.1786, 0.8214, 0.75], q:[0.3929, 1.2143], qb:[0.4286, 0.3929], phi:[0.3929]]	[M:[[3], [-3], [7]], q:[[1], [-2]], qb:[[-4], [1]], phi:[[1]]]	1

Relevant Operators	Marginal Operators	$n_{marginal}$$-$$|F_{IR}|$	Superconformal Index	Refined index
${}M_{3}$, ${ }\phi_{1}^{2}$, ${ }q_{1}\tilde{q}_{2}$, ${ }M_{2}$, ${ }\tilde{q}_{1}\tilde{q}_{2}$, ${ }M_{1}$, ${ }\phi_{1}\tilde{q}_{1}\tilde{q}_{2}$, ${ }M_{3}^{2}$, ${ }M_{3}\phi_{1}^{2}$, ${ }M_{3}q_{1}\tilde{q}_{2}$, ${ }M_{2}M_{3}$, ${ }\phi_{1}^{4}$, ${ }M_{3}\tilde{q}_{1}\tilde{q}_{2}$, ${ }q_{1}^{2}\tilde{q}_{2}^{2}$, ${ }M_{2}\phi_{1}^{2}$, ${ }q_{1}q_{2}$, ${ }M_{2}q_{1}\tilde{q}_{2}$, ${ }q_{2}\tilde{q}_{2}$, ${ }\phi_{1}^{2}\tilde{q}_{1}\tilde{q}_{2}$, ${ }q_{1}\tilde{q}_{1}\tilde{q}_{2}^{2}$, ${ }M_{2}^{2}$, ${ }q_{2}\tilde{q}_{1}$, ${ }M_{2}\tilde{q}_{1}\tilde{q}_{2}$, ${ }\tilde{q}_{1}^{2}\tilde{q}_{2}^{2}$, ${ }M_{1}M_{3}$, ${ }M_{1}\phi_{1}^{2}$, ${ }M_{3}\phi_{1}\tilde{q}_{1}\tilde{q}_{2}$	${}\phi_{1}^{3}\tilde{q}_{1}\tilde{q}_{2}$	-1	t^2.25 + 2*t^2.357 + 2*t^2.464 + t^3.536 + t^3.643 + t^4.5 + 2*t^4.607 + 4*t^4.714 + 5*t^4.821 + 4*t^4.929 + t^5.786 + t^5.893 - t^6. + t^6.75 + 2*t^6.857 + 4*t^6.964 + 7*t^7.071 + 6*t^7.179 + 5*t^7.286 + 5*t^7.393 + t^8.035 + t^8.143 - 2*t^8.25 - 4*t^8.357 - 7*t^8.464 - 2*t^8.572 - t^4.179/y - t^6.428/y - t^6.536/y + (2*t^7.607)/y + (3*t^7.714)/y + (5*t^7.821)/y + (2*t^7.929)/y - t^8.678/y + (2*t^8.893)/y - t^4.179*y - t^6.428*y - t^6.536*y + 2*t^7.607*y + 3*t^7.714*y + 5*t^7.821*y + 2*t^7.929*y - t^8.678*y + 2*t^8.893*y	g1^7*t^2.25 + 2*g1^2*t^2.357 + (2*t^2.464)/g1^3 + g1^3*t^3.536 + t^3.643/g1^2 + g1^14*t^4.5 + 2*g1^9*t^4.607 + 4*g1^4*t^4.714 + (5*t^4.821)/g1 + (4*t^4.929)/g1^6 + g1^10*t^5.786 + g1^5*t^5.893 - t^6. + g1^21*t^6.75 + 2*g1^16*t^6.857 + 4*g1^11*t^6.964 + 7*g1^6*t^7.071 + 6*g1*t^7.179 + (5*t^7.286)/g1^4 + (5*t^7.393)/g1^9 + g1^17*t^8.035 + g1^12*t^8.143 - 2*g1^7*t^8.25 - 4*g1^2*t^8.357 - (7*t^8.464)/g1^3 - (2*t^8.572)/g1^8 - (g1*t^4.179)/y - (g1^8*t^6.428)/y - (g1^3*t^6.536)/y + (2*g1^9*t^7.607)/y + (3*g1^4*t^7.714)/y + (5*t^7.821)/(g1*y) + (2*t^7.929)/(g1^6*y) - (g1^15*t^8.678)/y + (2*g1^5*t^8.893)/y - g1*t^4.179*y - g1^8*t^6.428*y - g1^3*t^6.536*y + 2*g1^9*t^7.607*y + 3*g1^4*t^7.714*y + (5*t^7.821*y)/g1 + (2*t^7.929*y)/g1^6 - g1^15*t^8.678*y + 2*g1^5*t^8.893*y

Deformation

Here is the data for the deformed fixed points from the chosen fixed point.

#	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational
467	${}\phi_{1}q_{1}q_{2}$ + ${ }M_{1}q_{1}\tilde{q}_{1}$ + ${ }M_{2}\phi_{1}\tilde{q}_{2}^{2}$ + ${ }M_{1}M_{2}$ + ${ }M_{1}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{3}\phi_{1}\tilde{q}_{1}^{2}$ + ${ }M_{3}^{2}$	0.4739	0.6079	0.7797	[M:[1.2857, 0.7143, 1.0], q:[0.4286, 1.1429], qb:[0.2857, 0.4286], phi:[0.4286]]	2*t^2.143 + 2*t^2.571 + t^3. + t^3.429 + t^3.857 + 4*t^4.286 + 5*t^4.714 + 4*t^5.143 + 2*t^5.571 - t^4.286/y - t^4.286*y	detail	{a: 2601/5488, c: 417/686, M1: 9/7, M2: 5/7, M3: 1, q1: 3/7, q2: 8/7, qb1: 2/7, qb2: 3/7, phi1: 3/7}
468	${}\phi_{1}q_{1}q_{2}$ + ${ }M_{1}q_{1}\tilde{q}_{1}$ + ${ }M_{2}\phi_{1}\tilde{q}_{2}^{2}$ + ${ }M_{1}M_{2}$ + ${ }M_{1}\tilde{q}_{1}\tilde{q}_{2}$ + ${ }M_{3}\phi_{1}\tilde{q}_{1}^{2}$ + ${ }M_{4}\phi_{1}\tilde{q}_{1}\tilde{q}_{2}$	0.5243	0.6766	0.775	[M:[1.1728, 0.8272, 0.7366, 0.7819], q:[0.3909, 1.2181], qb:[0.4362, 0.3909], phi:[0.3909]]	t^2.21 + 3*t^2.346 + 2*t^2.482 + t^3.518 + t^4.42 + 3*t^4.555 + 7*t^4.691 + 7*t^4.827 + 4*t^4.963 + t^5.728 + t^5.864 - 3*t^6. - t^4.173/y - t^4.173*y	detail

Equivalent Fixed Points from Other Seed Theories

Here is a list of equivalent fixed points from other gauge theories.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational

Equivalent Fixed Points from the Same Seed Theory

Below is a list of equivalent fixed points from the same seed theories.

id	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	More Info.	Rational

Previous Theory

The previous fixed point before deforming to get the chosen fixed point.

#	Theory	Superpotential	Central Charge $a$	Central Charge $c$	Ratio $a/c$	$R$-charges	Superconformal Index	More Info.	Rational
186	SU2adj1nf2	${}\phi_{1}q_{1}q_{2}$ + ${ }M_{1}q_{1}\tilde{q}_{1}$ + ${ }M_{2}\phi_{1}\tilde{q}_{2}^{2}$ + ${ }M_{1}M_{2}$ + ${ }M_{1}\tilde{q}_{1}\tilde{q}_{2}$	0.489	0.6143	0.7961	[M:[1.2024, 0.7976], q:[0.4008, 1.1984], qb:[0.3967, 0.4008], phi:[0.4008]]	2*t^2.393 + 2*t^2.405 + t^3.583 + t^3.595 + t^3.607 + 4*t^4.785 + 5*t^4.798 + 2*t^4.81 + 2*t^5.976 + 2*t^5.988 - t^6. - t^4.202/y - t^4.202*y	detail