The tzaddik sustains and blesses the world

במדרש שמעי בת וכו' משל בירה דולקת כו' ליפותך בעולם.

In the Midrash: "Hearken, daughter etc." (Tehillim 45:11) — the parable of the lit-up palace etc. — "to beautify you in the world."

The Sefas Emes draws on the famous Midrash of Avraham seeing a palace "lit up" (with fire/turmoil) and asking who its master is. He frames the question of why the wicked exist: it is "to beautify you" — the tzaddik — in the world.

פי' כי אברהם אבינו תמה איך הבורא ית' מניח את הרשעים לאבד עולמו והשיבו.

The explanation is that Avraham Avinu wondered how the Creator allows the wicked to destroy His world, and He answered him.

Avraham was troubled by the apparent contradiction: if Hashem rules the world, why does He permit the resha'im to ravage it? Hashem responds to this question.

כי הוא הצדיק שהעולם קיים עליו וא"ת למה נבראו הרשעים ליפותך בעולם כדי שיהי' שכר להצדיק שפורש עצמו מהם כמ"ש ושכחי עמך כו'.

For he is the tzaddik upon whom the world stands; and if you ask why the wicked were created — "to beautify you in the world," so that there be reward for the tzaddik who separates himself from them, as it is written: "and forget your people etc." (Tehillim 45:11).

Avraham is the tzaddik who upholds the world. The resha'im exist to "beautify" him — that is, to give him the merit of consciously separating himself from their ways, as the pasuk urges the soul to forget its former people and attachments.

ויתאו המלך יפיך כו' ומזה התענוג שניתוסף להבורא ית' מהצדיקים ע"י שהם בין הרשעים כשושנה בין החוחים עי"ז יש כח וקיום גם להרשעים והנה אברהם אע"ה תיקן כל הבריאה כמ"ש שהקנה להקב"ה שמים וארץ ונאמר לו ואעשך לגוי גדול ואברכה מברכיך כו' ולמה הבטיח לו כל זאת והלא בלא זה הי' עושה רצונו ית'.

"And the King will desire your beauty etc." (Tehillim 45:12) — and from this delight that is added to the Creator from the tzaddikim, by their being among the wicked like a rose among the thorns, through this there is power and existence even for the wicked. Now Avraham Avinu repaired all of creation, as it is said that he acquired heaven and earth for the Holy One; and he was told, "I will make you a great nation, and I will bless those who bless you etc." (Bereishis 12:2-3). And why did Hashem promise him all this — would he not have done His ratzon even without it?

The tzaddik's avodah amid the wicked — "a rose among the thorns" — brings Hashem delight, and that very delight grants the resha'im their continued existence. Avraham repaired all of creation and "acquired" heaven and earth for Hashem. The Sefas Emes then asks: since Avraham would have served Hashem regardless, why did he need all these promises of greatness and blessing?

אבל רצה להודיעו שידע כי הכל תלוי בו ושהוא הצדיק שהכל מתברכין בעבורו ולכן כל המעשים שעשה אאע"ה עשאהו בעבור כל הדורות הבאים וזהו ענין שם אבות שכל מעשיהם לא הי' לשעה וז"ש שאומרים אלקי אברהם יצחק כו'.

But He wished to inform him, that he should know that everything depends upon him and that he is the tzaddik through whom all are blessed; and therefore all the deeds that Avraham Avinu did, he did for the sake of all the generations to come. And this is the matter of the Avos — that all their deeds were not for a fleeting moment; and this is why we say "the God of Avraham, of Yitzchak etc."

The promises were not a reward but information: Hashem wanted Avraham to know that the whole world's blessing flows through him. The Avos' deeds were never temporary acts — they planted enduring spiritual power for all future generations, which is why we invoke Hashem as the God of each of the Avos.

פי' שקבלת מלכותו ית' שקיבלו עליהם עודנו קיים לכל זרע ישראל שבכחם יכולים גם הם לקבל אלקותו יתברך בהתעוררות מעשי אבות.

The explanation is that the acceptance of His kingship which they took upon themselves still endures for all the seed of Yisrael, so that through their power their descendants too are able to accept His Divinity, by means of the awakening of the deeds of the Avos.

When the Avos accepted Hashem's malchus, they established a permanent capacity in their descendants. Every Jew can still draw on the power of the Avos' deeds to accept Hashem's sovereignty anew.

וגם הראה לו ואברכה מברכיך שגם עי"ז יכול לקיים כל הבריאה שגם הרשעים שא"י להטות לבם אחר דרכו של אאע"ה אעפ"כ ע"י שיראו ויבינו כי הוא הצדיק ויברכו אותו יהי' להם ג"כ ברכה ועי"ז יהנו כולם ממנו:

And He also showed him, "and I will bless those who bless you," that through this too he can sustain all of creation — for even the wicked, who cannot incline their hearts after the way of Avraham Avinu, nevertheless, by seeing and understanding that he is the tzaddik and blessing him, they too will have blessing, and through this all will benefit from him.

The blessing "I will bless those who bless you" provides a second path of repair: even resha'im who cannot follow Avraham's path can still recognize his greatness and bless him. That recognition draws blessing down to them too, so that the entire world — even the wicked — benefits through the tzaddik.

Summary: The tzaddik upholds the world, and the wicked exist to "beautify" him by giving him the merit of separating from them; the delight this brings Hashem sustains even the resha'im. Avraham's deeds and the promises he received were meant to reveal that all blessing flows through the tzaddik — both directly, through the enduring power of the Avos that every Jew inherits, and indirectly, as even the wicked draw blessing by recognizing and blessing him.