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): 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): 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 symm + (conj.) (not completed) SU(9): 2 rank-2 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 Sp(2): 1 Adj + 2 fund Sp(2): 1 14 + 2 fund Sp(2): 2 Adj Sp(2): 1 Adj + 2 rank-2 anti-symm + 8 fund (not completed) G2: 1 Adj + 1 fund 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
55667	SU2adj1nf3	${}\phi_{1}q_{1}q_{2}$ + ${ }q_{2}q_{3}$ + ${ }q_{3}\tilde{q}_{1}$	0.6076	0.7195	0.8446	[q:[0.8211, 0.8211, 1.1789], qb:[0.8211, 0.4632, 0.4632], phi:[0.3578]]	[q:[[-1, 1, 1], [1, 0, 0], [-1, 0, 0]], qb:[[1, 0, 0], [0, 3, 0], [0, 0, 3]], phi:[[0, -1, -1]]]	3

Relevant Operators	Marginal Operators	$n_{marginal}$$-$$|F_{IR}|$	Superconformal Index	Refined index
${}\phi_{1}^{2}$, ${ }\tilde{q}_{2}\tilde{q}_{3}$, ${ }\tilde{q}_{1}\tilde{q}_{2}$, ${ }\phi_{1}\tilde{q}_{2}^{2}$, ${ }q_{1}\tilde{q}_{2}$, ${ }\phi_{1}\tilde{q}_{2}\tilde{q}_{3}$, ${ }\tilde{q}_{1}\tilde{q}_{3}$, ${ }q_{1}\tilde{q}_{3}$, ${ }\phi_{1}\tilde{q}_{3}^{2}$, ${ }\phi_{1}^{4}$, ${ }q_{1}\tilde{q}_{1}$, ${ }\phi_{1}^{2}\tilde{q}_{2}\tilde{q}_{3}$, ${ }\tilde{q}_{2}^{2}\tilde{q}_{3}^{2}$	${}\phi_{1}\tilde{q}_{1}^{2}$, ${ }\phi_{1}^{2}\tilde{q}_{1}\tilde{q}_{2}$, ${ }\phi_{1}^{3}\tilde{q}_{2}^{2}$, ${ }\phi_{1}^{2}\tilde{q}_{1}\tilde{q}_{3}$, ${ }\phi_{1}^{3}\tilde{q}_{2}\tilde{q}_{3}$, ${ }\phi_{1}^{3}\tilde{q}_{3}^{2}$	-2	t^2.147 + t^2.779 + 7*t^3.853 + t^4.294 + 2*t^4.926 + t^5.559 - 2*t^6. + t^6.441 + 7*t^6.632 - 6*t^7.074 + 21*t^7.706 - t^8.147 + t^8.338 + t^8.588 - 3*t^8.779 - t^4.074/y - t^6.221/y + (2*t^7.926)/y - t^8.368/y - t^4.074*y - t^6.221*y + 2*t^7.926*y - t^8.368*y	t^2.147/(g2^2*g3^2) + g2^3*g3^3*t^2.779 + g1*g2^3*t^3.853 + (g2^5*t^3.853)/g3 + (g2^4*g3*t^3.853)/g1 + g2^2*g3^2*t^3.853 + g1*g3^3*t^3.853 + (g2*g3^4*t^3.853)/g1 + (g3^5*t^3.853)/g2 + t^4.294/(g2^4*g3^4) + 2*g2*g3*t^4.926 + g2^6*g3^6*t^5.559 - 2*t^6. + t^6.441/(g2^6*g3^6) + g2^8*g3^2*t^6.632 + g1*g2^6*g3^3*t^6.632 + (g2^7*g3^4*t^6.632)/g1 + g2^5*g3^5*t^6.632 + g1*g2^3*g3^6*t^6.632 + (g2^4*g3^7*t^6.632)/g1 + g2^2*g3^8*t^6.632 - (g1*t^7.074)/g2^3 - (g2^2*t^7.074)/g3^4 - (g1*t^7.074)/g3^3 - (g2*t^7.074)/(g1*g3^2) - (g3*t^7.074)/(g1*g2^2) - (g3^2*t^7.074)/g2^4 + g1^2*g2^6*t^7.706 + (g2^9*t^7.706)/g1 + (g2^10*t^7.706)/g3^2 + (g1*g2^8*t^7.706)/g3 + g2^7*g3*t^7.706 + g1*g2^5*g3^2*t^7.706 + (g2^8*g3^2*t^7.706)/g1^2 + g1^2*g2^3*g3^3*t^7.706 + (g2^6*g3^3*t^7.706)/g1 + 3*g2^4*g3^4*t^7.706 + g1*g2^2*g3^5*t^7.706 + (g2^5*g3^5*t^7.706)/g1^2 + g1^2*g3^6*t^7.706 + (g2^3*g3^6*t^7.706)/g1 + g2*g3^7*t^7.706 + (g1*g3^8*t^7.706)/g2 + (g2^2*g3^8*t^7.706)/g1^2 + (g3^9*t^7.706)/g1 + (g3^10*t^7.706)/g2^2 - t^8.147/(g2^2*g3^2) + g2^9*g3^9*t^8.338 + t^8.588/(g2^8*g3^8) - 3*g2^3*g3^3*t^8.779 - t^4.074/(g2*g3*y) - t^6.221/(g2^3*g3^3*y) + (2*g2*g3*t^7.926)/y - t^8.368/(g2^5*g3^5*y) - (t^4.074*y)/(g2*g3) - (t^6.221*y)/(g2^3*g3^3) + 2*g2*g3*t^7.926*y - (t^8.368*y)/(g2^5*g3^5)

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
55723	${}\phi_{1}q_{1}q_{2}$ + ${ }q_{2}q_{3}$ + ${ }q_{3}\tilde{q}_{1}$ + ${ }M_{1}\tilde{q}_{1}\tilde{q}_{2}$	0.6281	0.7582	0.8284	[M:[0.6941], q:[0.81, 0.8347, 1.1653], qb:[0.8347, 0.4712, 0.463], phi:[0.3553]]	t^2.082 + t^2.132 + t^2.803 + t^3.819 + 2*t^3.844 + t^3.868 + 2*t^3.893 + t^4.165 + t^4.214 + t^4.263 + t^4.885 + 2*t^4.934 + t^5.605 + t^5.901 + 2*t^5.926 + t^5.951 + 2*t^5.975 - 2*t^6. - t^4.066/y - t^4.066*y	detail
55736	${}\phi_{1}q_{1}q_{2}$ + ${ }q_{2}q_{3}$ + ${ }q_{3}\tilde{q}_{1}$ + ${ }M_{1}\tilde{q}_{2}\tilde{q}_{3}$ + ${ }\phi_{1}^{2}X_{1}$	0.5833	0.6667	0.875	[X:[1.3333], M:[1.0], q:[0.8333, 0.8333, 1.1667], qb:[0.8333, 0.5, 0.5], phi:[0.3333]]	t^3. + 8*t^4. + t^5. - 8*t^6. - t^4./y - t^4.*y	detail	{a: 7/12, c: 2/3, X1: 4/3, M1: 1, q1: 5/6, q2: 5/6, q3: 7/6, qb1: 5/6, qb2: 1/2, qb3: 1/2, phi1: 1/3}

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
39	SU2adj1nf2	${}\phi_{1}q_{1}q_{2}$	0.6076	0.7195	0.8446	[q:[0.8211, 0.8211], qb:[0.4632, 0.4632], phi:[0.3578]]	t^2.147 + t^2.779 + 7*t^3.853 + t^4.294 + 2*t^4.926 + t^5.559 - 2*t^6. - t^4.074/y - t^4.074*y	detail

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
55448	SU2adj1nf3	${}\phi_{1}q_{1}q_{2}$ + ${ }q_{2}q_{3}$	0.7103	0.8462	0.8394	[q:[0.5651, 1.0, 1.0], qb:[0.5651, 0.5651, 0.5651], phi:[0.4349]]	t^2.61 + 6*t^3.39 + 10*t^4.695 + t^5.219 - 10*t^6. - t^4.305/y - t^4.305*y	detail